Bibliography Bibliography C Bibliography E

Bibliography D

G. M. D’Ariano, C. Macchiavello, and M. G. A. Paris (1994) Detection of the density matrix through optical homodyne tomography without filtered back projection. Phys. Rev. A 50 (5), pp. 4298–4302.
ⓘ

External Links:

Document

Referenced by:

§13.28(iii).

Encodings:

BibTeX
M. D’Ocagne (1904) Sur une classe de nombres rationnels réductibles aux nombres de Bernoulli. Bull. Sci. Math. (2) 28, pp. 29–32 (French).
ⓘ

External Links:

ZentralBlatt

Referenced by:

§24.1.

Encodings:

BibTeX
D. Dai, M. E. H. Ismail, and X. Wang (2014) Plancherel-Rotach asymptotic expansion for some polynomials from indeterminate moment problems. Constr. Approx. 40 (1), pp. 61–104.
ⓘ

External Links:

ISSN 0176-4276, Document, Link, MathReview (Francisco Marcellán), ZentralBlatt

Referenced by:

§2.9(iii), §2.9(iii).

Encodings:

BibTeX
H. Davenport (2000) Multiplicative Number Theory. 3rd edition, Graduate Texts in Mathematics, Vol. 74, Springer-Verlag, New York.
ⓘ

Notes:

Revised and with a preface by Hugh L. Montgomery

External Links:

ISBN 0-387-95097-4, MathReview, ZentralBlatt

Referenced by:

§27.12.

Encodings:

BibTeX
B. Davies (1973) Complex zeros of linear combinations of spherical Bessel functions and their derivatives. SIAM J. Math. Anal. 4 (1), pp. 128–133.
ⓘ

External Links:

ISSN 1095-7154, Document, MathReview (C. J. Bouwkamp), ZentralBlatt

Referenced by:

§10.58.

Encodings:

BibTeX
B. Davies (1984) Integral Transforms and their Applications. 2nd edition, Applied Mathematical Sciences, Vol. 25, Springer-Verlag, New York.
ⓘ

External Links:

ISBN 0-387-96080-5, MathReview, ZentralBlatt

Referenced by:

§1.14(vii).

Encodings:

BibTeX
H. T. Davis (1933) Tables of Higher Mathematical Functions I. Principia Press, Bloomington, Indiana.
ⓘ

External Links:

ZentralBlatt

Referenced by:

§5.1, Notations P.

Encodings:

BibTeX
H. F. Davis and A. D. Snider (1987) Introduction to Vector Analysis. 5th edition, Allyn and Bacon Inc., Boston, MA.
ⓘ

Notes:

Seventh edition printed by WCB/McGraw-Hill, 1995.

External Links:

ISBN 0-697-06356-9; 0-697-16099-8, MathReview (R. H. Bowman), ZentralBlatt

Referenced by:

§1.5(ii).

Encodings:

BibTeX
P. J. Davis and P. Rabinowitz (1984) Methods of Numerical Integration. 2nd edition, Computer Science and Applied Mathematics, Academic Press Inc., Orlando, FL.
ⓘ

External Links:

ISBN 0-12-206360-0, MathReview (John P. Coleman), ZentralBlatt

Referenced by:

§3.5(iii), §3.5(i), §3.5(i), §3.5(ii), §3.5(iii), §3.5(iv), §3.5(v), §3.5(vi), §3.5(vii), §3.5(x).

Encodings:

BibTeX
P. J. Davis (1975) Interpolation and Approximation. Dover Publications Inc., New York.
ⓘ

Notes:

Republication of the original 1963 edition (Blaisdell Publishing Co.), with minor corrections and a new preface and bibliography

External Links:

MathReview, ZentralBlatt

Referenced by:

§3.3(i), §3.3(iii), §3.3(iv), §3.3(vi).

Encodings:

BibTeX
S. D. Daymond (1955) The principal frequencies of vibrating systems with elliptic boundaries. Quart. J. Mech. Appl. Math. 8 (3), pp. 361–372.
ⓘ

External Links:

Document, MathReview (M. A. Hyman), ZentralBlatt

Referenced by:

3rd item.

Encodings:

BibTeX
C. de Boor (2001) A Practical Guide to Splines. Revised edition, Applied Mathematical Sciences, Vol. 27, Springer-Verlag, New York.
ⓘ

External Links:

ISBN 0-387-95366-3, MathReview (Gerlind Plonka-Hoch), ZentralBlatt

Referenced by:

§3.11(vi).

Encodings:

BibTeX
L. de Branges (1985) A proof of the Bieberbach conjecture. Acta Math. 154 (1-2), pp. 137–152.
ⓘ

External Links:

ISSN 0001-5962, Document, MathReview (P. L. Duren), ZentralBlatt

Referenced by:

§16.23(iii), §18.38(ii).

Encodings:

BibTeX
N. G. de Bruijn (1937) Integralen voor de $\zeta$ -functie van Riemann. Mathematica (Zutphen) B5, pp. 170–180 (Dutch).
ⓘ

Notes:

In Dutch.

External Links:

ZentralBlatt

Referenced by:

(25.5.15), (25.5.16), (25.5.17), (25.5.18), (25.5.19), §25.5(ii).

Encodings:

BibTeX
N. G. de Bruijn (1961) Asymptotic Methods in Analysis. 2nd edition, Bibliotheca Mathematica, Vol. IV, North-Holland Publishing Co., Amsterdam.
ⓘ

External Links:

MathReview, ZentralBlatt

Referenced by:

§2.2, Ch.2, §26.7(iv), §26.7(iv), §4.13.

Encodings:

BibTeX
N. G. de Bruijn (1981) Pólya’s Theory of Counting. In Applied Combinatorial Mathematics, E. F. Beckenbach (Ed.), pp. 144–184.
ⓘ

External Links:

ISBN 0898741726

Referenced by:

§26.20.

Encodings:

BibTeX
M. G. de Bruin, E. B. Saff, and R. S. Varga (1981a) On the zeros of generalized Bessel polynomials. I. Nederl. Akad. Wetensch. Indag. Math. 84 (1), pp. 1–13.
ⓘ

External Links:

ISSN 0019-3577, Document, MathReview (M. E. Muldoon), ZentralBlatt

Referenced by:

§10.49(ii), §10.58.

Encodings:

BibTeX
M. G. de Bruin, E. B. Saff, and R. S. Varga (1981b) On the zeros of generalized Bessel polynomials. II. Nederl. Akad. Wetensch. Indag. Math. 84 (1), pp. 14–25.
ⓘ

External Links:

ISSN 0019-3577, Document, MathReview (M. E. Muldoon), ZentralBlatt

Referenced by:

§10.49(ii), §10.58.

Encodings:

BibTeX
C. de la Vallée Poussin (1896a) Recherches analytiques sur la théorie des nombres premiers. Première partie. La fonction $\zeta(s)$ de Riemann et les nombres premiers en général, suivi d’un Appendice sur des réflexions applicables à une formule donnée par Riemann. Ann. Soc. Sci. Bruxelles 20, pp. 183–256 (French).
ⓘ

Notes:

Reprinted in Collected works/Oeuvres scientifiques, Vol. I, pp. 223–296 Académie Royale de Belgique, Brussels, 2000.

External Links:

MathReview, ZentralBlatt

Referenced by:

§25.10(i), §27.11, §27.2(i).

Encodings:

BibTeX
C. de la Vallée Poussin (1896b) Recherches analytiques sur la théorie des nombres premiers. Deuxième partie. Les fonctions de Dirichlet et les nombres premiers de la forme linéaire $Mx+N$ . Ann. Soc. Sci. Bruxelles 20, pp. 281–397 (French).
ⓘ

Notes:

Reprinted in Collected works/Oeuvres scientifiques, Vol. I, pp. 309–425, Académie Royale de Belgique, Brussels, 2000.

External Links:

MathReview, ZentralBlatt

Referenced by:

§25.10(i), §27.11, §27.2(i).

Encodings:

BibTeX
A. de-Shalit and I. Talmi (1963) Nuclear Shell Theory. Pure and Applied Physics, Vol. 14, Academic Press, New York.
ⓘ

Notes:

Reprinted by Dover Publications Inc., New York, 2004.

External Links:

ISBN 0-486-43933-X, MathReview (D. J. Thouless)

Referenced by:

§34.12, §34.3(i), §34.3(iv), §34.4, §34.5(i), §34.5(vi), §34.6, §34.7(i), §34.7(vi), Ch.34.

Encodings:

BibTeX
P. Dean (1966) The constrained quantum mechanical harmonic oscillator. Proc. Cambridge Philos. Soc. 62, pp. 277–286.
ⓘ

External Links:

Document, MathReview (T. Erber)

Referenced by:

§12.11(i), §12.11(i), §12.17.

Encodings:

BibTeX
A. Deaño, E. J. Huertas, and F. Marcellán (2013) Strong and ratio asymptotics for Laguerre polynomials revisited. J. Math. Anal. Appl. 403 (2), pp. 477–486.
ⓘ

External Links:

ISSN 0022-247X, Document, FullText, MathReview (Pablo Manuel Román), ZentralBlatt

Referenced by:

§18.15(iv), §18.15(iv).

Encodings:

BibTeX
A. Deaño, J. Segura, and N. M. Temme (2010) Computational properties of three-term recurrence relations for Kummer functions. J. Comput. Appl. Math. 233 (6), pp. 1505–1510.
ⓘ

External Links:

ISSN 0377-0427, Document, FullText, MathReview (Richard B. Paris), ZentralBlatt

Referenced by:

§13.29(iv), §13.29(iv).

Encodings:

BibTeX
S. R. Deans (1983) The Radon Transform and Some of Its Applications. A Wiley-Interscience Publication, John Wiley & Sons Inc., New York.
ⓘ

Notes:

Reprinted by Dover in 2007.

External Links:

ISBN 0-471-89804-X, MathReview (W. R. Madych), ZentralBlatt

Referenced by:

§18.38(ii).

Encodings:

BibTeX
L. Debnath and D. Bhatta (2015) Integral transforms and their applications. Third edition, CRC Press, Boca Raton, FL.
ⓘ

External Links:

ISBN 978-1-4822-2357-6, MathReview Entry, ZentralBlatt

Referenced by:

§1.16(viii).

Encodings:

BibTeX
A. Debosscher (1998) Unification of one-dimensional Fokker-Planck equations beyond hypergeometrics: Factorizer solution method and eigenvalue schemes. Phys. Rev. E (3) 57 (1), pp. 252–275.
ⓘ

External Links:

ISSN 1063-651X, Document, MathReview (Victor I. Stepanov), ZentralBlatt

Referenced by:

§31.17(ii).

Encodings:

BibTeX
A. Decarreau, M.-Cl. Dumont-Lepage, P. Maroni, A. Robert, and A. Ronveaux (1978a) Formes canoniques des équations confluentes de l’équation de Heun. Ann. Soc. Sci. Bruxelles Sér. I 92 (1-2), pp. 53–78.
ⓘ

External Links:

MathReview (A. E. Danese), ZentralBlatt

Referenced by:

§31.12.

Encodings:

BibTeX
A. Decarreau, P. Maroni, and A. Robert (1978b) Sur les équations confluentes de l’équation de Heun. Ann. Soc. Sci. Bruxelles Sér. I 92 (3), pp. 151–189.
ⓘ

External Links:

ISSN 0037-959X, MathReview, ZentralBlatt

Referenced by:

§31.12.

Encodings:

BibTeX
B. Deconinck, M. Heil, A. Bobenko, M. van Hoeij, and M. Schmies (2004) Computing Riemann theta functions. Math. Comp. 73 (247), pp. 1417–1442.
ⓘ

Notes:

Two of the authors (Deconinck and van Hoeij) have developed Maple code for the algorithms described in this paper.

External Links:

ISSN 0025-5718, Document, Code, MathReview, ZentralBlatt

Referenced by:

§21.10(i), 1st item, §21.2(i), §21.4, M. Heil (1995).

Encodings:

BibTeX
B. Deconinck and J. N. Kutz (2006) Computing spectra of linear operators using the Floquet-Fourier-Hill method. J. Comput. Phys. 219 (1), pp. 296–321.
ⓘ

External Links:

ISSN 0021-9991, MathReview, ZentralBlatt

Referenced by:

§22.11.

Encodings:

BibTeX
B. Deconinck and H. Segur (1998) The KP equation with quasiperiodic initial data. Phys. D 123 (1-4), pp. 123–152.
ⓘ

Notes:

Nonlinear waves and solitons in physical systems (Los Alamos, NM, 1997)

External Links:

ISSN 0167-2789, Document, MathReview (Pavel Krejčí), ZentralBlatt

Referenced by:

§21.9.

Encodings:

BibTeX
B. Deconinck and H. Segur (2000) Pole dynamics for elliptic solutions of the Korteweg-de Vries equation. Math. Phys. Anal. Geom. 3 (1), pp. 49–74.
ⓘ

External Links:

ISSN 1385-0172, Document, MathReview (Giulio Soliani), ZentralBlatt

Referenced by:

§23.21(ii).

Encodings:

BibTeX
B. Deconinck and M. van Hoeij (2001) Computing Riemann matrices of algebraic curves. Phys. D 152/153, pp. 28–46.
ⓘ

External Links:

ISSN 0167-2789, Document, MathReview (John B. Little), ZentralBlatt

Referenced by:

3rd item.

Encodings:

BibTeX
P. A. Deift and X. Zhou (1995) Asymptotics for the Painlevé II equation. Comm. Pure Appl. Math. 48 (3), pp. 277–337.
ⓘ

External Links:

ISSN 0010-3640, MathReview (Alexander Vladimirovich Kitaev), ZentralBlatt

Referenced by:

§32.11(ii), §32.11(iii).

Encodings:

BibTeX
P. A. Deift (1998) Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach. Courant Lecture Notes in Mathematics, Vol. 3, New York University Courant Institute of Mathematical Sciences, New York.
ⓘ

External Links:

ISBN 0-9658703-2-4; 0-8218-2695-6, MathReview (Alexander Vladimirovich Kitaev), ZentralBlatt

Referenced by:

§18.38(ii), §18.38(ii).

Encodings:

BibTeX
P. Deift, T. Kriecherbauer, K. T. McLaughlin, S. Venakides, and X. Zhou (1999a) Strong asymptotics of orthogonal polynomials with respect to exponential weights. Comm. Pure Appl. Math. 52 (12), pp. 1491–1552.
ⓘ

External Links:

ISSN 0010-3640, Document, MathReview (D. S. Lubinsky), ZentralBlatt

Referenced by:

§18.32.

Encodings:

BibTeX
P. Deift, T. Kriecherbauer, K. T.-R. McLaughlin, S. Venakides, and X. Zhou (1999b) Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory. Comm. Pure Appl. Math. 52 (11), pp. 1335–1425.
ⓘ

External Links:

ISSN 0010-3640, Document, MathReview (D. S. Lubinsky), ZentralBlatt

Referenced by:

§18.32.

Encodings:

BibTeX
L. Dekar, L. Chetouani, and T. F. Hammann (1999) Wave function for smooth potential and mass step. Phys. Rev. A 59 (1), pp. 107–112.
ⓘ

External Links:

Document

Referenced by:

§15.18.

Encodings:

BibTeX
K. Dekker and J. G. Verwer (1984) Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations. CWI Monographs, Vol. 2, North-Holland Publishing Co., Amsterdam.
ⓘ

External Links:

ISBN 0-444-87634-0, MathReview (A. de Castro Brzezicki), ZentralBlatt

Referenced by:

§3.7(v).

Encodings:

BibTeX
H. Delange (1987) Sur les zéros imaginaires des polynômes de Bernoulli. C. R. Acad. Sci. Paris Sér. I Math. 304 (6), pp. 147–150 (French).
ⓘ

External Links:

ISSN 0249-6291, MathReview, ZentralBlatt

Referenced by:

§24.12(iii).

Encodings:

BibTeX
H. Delange (1988) On the real roots of Euler polynomials. Monatsh. Math. 106 (2), pp. 115–138.
ⓘ

External Links:

ISSN 0026-9255, MathReview (H. M. Srivastava), ZentralBlatt

Referenced by:

§24.12(ii).

Encodings:

BibTeX
H. Delange (1991) Sur les zéros réels des polynômes de Bernoulli. Ann. Inst. Fourier (Grenoble) 41 (2), pp. 267–309 (French).
ⓘ

External Links:

ISSN 0373-0956, MathReview (F. Beukers), ZentralBlatt

Referenced by:

§24.12(i).

Encodings:

BibTeX
M. Deléglise and J. Rivat (1996) Computing $\pi(x)$ : The Meissel, Lehmer, Lagarias, Miller, Odlyzko method. Math. Comp. 65 (213), pp. 235–245.
ⓘ

External Links:

ISSN 0025-5718, Document, MathReview (Andrew Granville), ZentralBlatt

Referenced by:

§27.18.

Encodings:

BibTeX
Delft Numerical Analysis Group (1973) On the computation of Mathieu functions. J. Engrg. Math. 7, pp. 39–61.
ⓘ

Notes:

Variable-precision Algol program, maximum precision 15D

External Links:

Document, MathReview (C. J. Bouwkamp), ZentralBlatt

Referenced by:

§28.36(ii), §28.36(iii).

Encodings:

BibTeX
G. Delic (1979a) Chebyshev expansion of the associated Legendre polynomial $P^{M}_{L}(x)$ . Comput. Phys. Comm. 18 (1), pp. 63–71.
ⓘ

Notes:

Double-precision Fortran, maximum accuracy 25D

External Links:

Document, Code

Referenced by:

3rd item.

Encodings:

BibTeX
G. Delic (1979b) Chebyshev series for the spherical Bessel function $j_{l}(r)$ . Comput. Phys. Comm. 18 (1), pp. 73–86.
ⓘ

External Links:

Document

Referenced by:

§10.76(iii).

Encodings:

BibTeX
P. Deligne, P. Etingof, D. S. Freed, D. Kazhdan, J. W. Morgan, and D. R. Morrison (Eds.) (1999) Quantum Fields and Strings: A Course for Mathematicians. Vol. 1, 2. American Mathematical Society, Providence, RI.
ⓘ

Notes:

Material from the Special Year on Quantum Field Theory held at the Institute for Advanced Study, Princeton, NJ, 1996–1997

External Links:

ISBN 0-8218-1198-3, MathReview, ZentralBlatt

Referenced by:

§21.9.

Encodings:

BibTeX
J. Deltour (1968) The computation of lattice frequency distribution functions by means of continued fractions. Physica 39 (3), pp. 413–423.
ⓘ

External Links:

ISSN 0031-8914, Document, Link

Referenced by:

§18.40(ii).

Encodings:

BibTeX
J. Demmel and P. Koev (2006) Accurate and efficient evaluation of Schur and Jack functions. Math. Comp. 75 (253), pp. 223–239.
ⓘ

Notes:

For Fortran software for these functions, see Plamen Koev’s home page.

External Links:

Home Page, ISSN 0025-5718, Document, MathReview Entry, ZentralBlatt

Referenced by:

1st item.

Encodings:

BibTeX
J. B. Dence and T. P. Dence (1999) Elements of the Theory of Numbers. Harcourt/Academic Press, San Diego, CA.
ⓘ

External Links:

ISBN 0-12-209130-2, MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

Ch.24.

Encodings:

BibTeX
Derive (commercial interactive system) Texas Instruments, Inc..
ⓘ

Notes:

Symbolic and extended-precision numerical computing system.

Referenced by:

§ ‣ Software Cross Index, § ‣ Software Cross Index.

Encodings:

BibTeX
R. C. Desai and M. Nelkin (1966) Atomic motions in a rigid sphere gas as a problem in neutron transport. Nucl. Sci. Eng. 24 (2), pp. 142–152.
ⓘ

Referenced by:

§18.39(iii).

Encodings:

BibTeX
R. L. Devaney (1986) An Introduction to Chaotic Dynamical Systems. The Benjamin/Cummings Publishing Co. Inc., Menlo Park, CA.
ⓘ

External Links:

ISBN 0-8053-1601-9, MathReview (Richard C. Churchill), ZentralBlatt

Referenced by:

§3.8(viii).

Encodings:

BibTeX
J. Dexter and E. Agol (2009) A fast new public code for computing photon orbits in a Kerr spacetime. The Astrophysical Journal 696, pp. 1616–1629.
ⓘ

External Links:

Document

Referenced by:

§19.35(ii).

Encodings:

BibTeX
S. C. Dhar (1940) Note on the addition theorem of parabolic cylinder functions. J. Indian Math. Soc. (N. S.) 4, pp. 29–30.
ⓘ

External Links:

MathReview (M. C. Gray), ZentralBlatt

Referenced by:

§12.13(ii).

Encodings:

BibTeX
P. Di Francesco, P. Ginsparg, and J. Zinn-Justin (1995) $2$ D gravity and random matrices. Phys. Rep. 254 (1-2), pp. 1–133.
ⓘ

External Links:

ISSN 0370-1573, Document, MathReview (Yolanda Lozano)

Referenced by:

§32.16.

Encodings:

BibTeX
L. E. Dickson (1919) History of the Theory of Numbers (3 volumes). Carnegie Institution of Washington, Washington, D.C..
ⓘ

Notes:

Reprinted by Chelsea Publishing Co., New York, 1966.

External Links:

MathReview, ZentralBlatt

Referenced by:

§27.21.

Encodings:

BibTeX
A. R. DiDonato and A. H. Morris (1986) Computation of the incomplete gamma function ratios and their inverses. ACM Trans. Math. Software 12 (4), pp. 377–393.
ⓘ

External Links:

ISSN 0098-3500, Document, ZentralBlatt

Referenced by:

§8.12, §8.25(iii).

Encodings:

BibTeX
A. R. DiDonato and A. H. Morris (1987) Algorithm 654: Fortran subroutines for computing the incomplete gamma function ratios and their inverses. ACM Trans. Math. Software 13 (3), pp. 318–319.
ⓘ

Notes:

Single-precision Fortran, maximum accuracy 14D.

External Links:

ISSN 0098-3500, Document, GAMS (module 654; package TOMS), ZentralBlatt

Referenced by:

1st item.

Encodings:

BibTeX
A. R. DiDonato and A. H. Morris (1992) Algorithm 708: Significant digit computation of the incomplete beta function ratios. ACM Trans. Math. Software 18 (3), pp. 360–373.
ⓘ

Notes:

Single-precision Fortran, maximum accuracy 14D.

External Links:

ISSN 0098-3500, Document, GAMS (module 708; package TOMS), ZentralBlatt

Referenced by:

3rd item.

Encodings:

BibTeX
A. R. DiDonato (1978) An approximation for $\smallint^{\infty}_{\chi}e^{-t^{2}/2}t^{p}dt,$ $\chi>0,$ $p$ real. Math. Comp. 32 (141), pp. 271–275.
ⓘ

External Links:

FullText, MathReview (H. E. Fettis), ZentralBlatt

Referenced by:

1st item.

Encodings:

BibTeX
P. Dienes (1931) The Taylor Series. Oxford University Press, Oxford.
ⓘ

Notes:

Reprinted by Dover Publications Inc., New York, 1957

External Links:

MathReview, ZentralBlatt

Referenced by:

§1.9(iii).

Encodings:

BibTeX
A. Dienstfrey and J. Huang (2006) Integral representations for elliptic functions. J. Math. Anal. Appl. 316 (1), pp. 142–160.
ⓘ

External Links:

ISSN 0022-247X, Document, MathReview Entry, ZentralBlatt

Referenced by:

§23.11.

Encodings:

BibTeX
K. Dilcher, L. Skula, and I. Sh. Slavutskiǐ (1991) Bernoulli Numbers. Bibliography (1713–1990). Queen’s Papers in Pure and Applied Mathematics, Vol. 87, Queen’s University, Kingston, ON.
ⓘ

Notes:

A frequently updated version, with links to reviews, exists online

External Links:

Online version, MathReview, ZentralBlatt

Referenced by:

Ch.24.

Encodings:

BibTeX
K. Dilcher (1987a) Asymptotic behaviour of Bernoulli, Euler, and generalized Bernoulli polynomials. J. Approx. Theory 49 (4), pp. 321–330.
ⓘ

External Links:

ISSN 0021-9045, Document, MathReview (Guillermo López Lagomasino), ZentralBlatt

Referenced by:

§24.11.

Encodings:

BibTeX
K. Dilcher (1987b) Irreducibility of certain generalized Bernoulli polynomials belonging to quadratic residue class characters. J. Number Theory 25 (1), pp. 72–80.
ⓘ

External Links:

ISSN 0022-314X, Document, MathReview (T. Metsänkylä)

Referenced by:

§24.12(iii).

Encodings:

BibTeX
K. Dilcher (1988) Zeros of Bernoulli, generalized Bernoulli and Euler polynomials. Mem. Amer. Math. Soc. 73 (386), pp. iv+94.
ⓘ

External Links:

ISSN 0065-9266, MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§24.12(i), §24.12(iii), §24.16(ii).

Encodings:

BibTeX
K. Dilcher (1996) Sums of products of Bernoulli numbers. J. Number Theory 60 (1), pp. 23–41.
ⓘ

External Links:

ISSN 0022-314X, Document, MathReview (Wen Peng Zhang), ZentralBlatt

Referenced by:

§24.14(ii).

Encodings:

BibTeX
K. Dilcher (2002) Bernoulli Numbers and Confluent Hypergeometric Functions. In Number Theory for the Millennium, I (Urbana, IL, 2000), pp. 343–363.
ⓘ

External Links:

ISBN 1-56881-126-8, MathReview (Arnold M. Adelberg), ZentralBlatt

Referenced by:

§24.16(iii).

Encodings:

BibTeX
K. Dilcher (2008) On multiple zeros of Bernoulli polynomials. Acta Arith. 134 (2), pp. 149–155.
ⓘ

External Links:

ISSN 0065-1036, Document, MathReview (Arnold M. Adelberg), ZentralBlatt

Referenced by:

§24.12(iv).

Encodings:

BibTeX

D. K. Dimitrov and G. P. Nikolov (2010) Sharp bounds for the extreme zeros of classical orthogonal polynomials. J. Approx. Theory 162 (10), pp. 1793–1804.
ⓘ

External Links:

ISSN 0021-9045, Document, FullText, MathReview (Francisco Marcellán), ZentralBlatt

Referenced by:

(18.16.12), (18.16.13), §18.16(ii), §18.16(ii), §18.16(iv).

Encodings:

BibTeX
A. M. Din (1981) A simple sum formula for Clebsch-Gordan coefficients. Lett. Math. Phys. 5 (3), pp. 207–211.
ⓘ

External Links:

ISSN 0377-9017, Document, MathReview, ZentralBlatt

Referenced by:

§14.17(iv).

Encodings:

BibTeX
D. Ding (2000) A simplified algorithm for the second-order sound fields. J. Acoust. Soc. Amer. 108 (6), pp. 2759–2764.
ⓘ

External Links:

Document

Referenced by:

§8.24(iii).

Encodings:

BibTeX
H. Ding, K. I. Gross, and D. St. P. Richards (1996) Ramanujan’s master theorem for symmetric cones. Pacific J. Math. 175 (2), pp. 447–490.
ⓘ

External Links:

ISSN 0030-8730, MathReview (Jacques Faraut), ZentralBlatt

Referenced by:

§35.7(ii), §35.8(iv), §35.8(v).

Encodings:

BibTeX
R. B. Dingle (1957a) The Bose-Einstein integrals ${\mathscr{B}}_{p}(\eta)=(p!)^{-1}\int^{\infty}_{0}\epsilon^{p}(e^{\epsilon-% \eta}-1)^{-1}d\epsilon$ . Appl. Sci. Res. B. 6, pp. 240–244.
ⓘ

External Links:

ISSN 0003-6994, MathReview Entry, ZentralBlatt

Referenced by:

(25.12.15), §25.12(iii), §25.12.

Encodings:

BibTeX
R. B. Dingle (1957b) The Fermi-Dirac integrals ${\mathscr{F}}_{p}(\eta)=(p!)^{-1}\int^{\infty}_{0}\epsilon^{p}(e^{\epsilon-% \eta}+1)^{-1}d\epsilon$ . Appl. Sci. Res. B. 6, pp. 225–239.
ⓘ

External Links:

ISSN 0003-6994, MathReview Entry, ZentralBlatt

Referenced by:

(25.12.14), §25.12(iii), §25.12.

Encodings:

BibTeX
R. B. Dingle (1973) Asymptotic Expansions: Their Derivation and Interpretation. Academic Press, London-New York.
ⓘ

External Links:

MathReview, ZentralBlatt

Referenced by:

(11.11.11), §11.6(i), §11.6(iii), §2.11(v), Ch.2, §8.1, Notations, Notations.

Encodings:

BibTeX
P. G. L. Dirichlet (1837) Beweis des Satzes, dass jede unbegrenzte arithmetische Progression, deren erstes Glied und Differenz ganze Zahlen ohne gemeinschaftlichen Factor sind, unendlich viele Primzahlen enthält. Abhandlungen der Königlich Preussischen Akademie der Wissenschaften von 1837, pp. 45–81 (German).
ⓘ

Notes:

Reprinted in G. Lejeune Dirichlet’s Werke, Band I, pp. 313–342, Reimer, Berlin, 1889 and with corrections in G. Lejeune Dirichlet’s Werke, AMS Chelsea Publishing Series, Providence, RI, 1969.

External Links:

ISBN 0-8284-0225-6, Link, MathReview

Referenced by:

§25.15(i).

Encodings:

BibTeX
P. G. L. Dirichlet (1849) Über die Bestimmung der mittleren Werthe in der Zahlentheorie. Abhandlungen der Königlich Preussischen Akademie der Wissenschaften von 1849, pp. 69–83 (German).
ⓘ

Notes:

Reprinted in G. Lejeune Dirichlet’s Werke, Band II, pp. 49–66, Reimer, Berlin, 1897 and with corrections in G. Lejeune Dirichlet’s Werke, AMS Chelsea Publishing Series, Providence, RI, 1969.

External Links:

ISBN 0-8284-0225-6, Link, MathReview

Referenced by:

§27.11.

Encodings:

BibTeX
A. L. Dixon and W. L. Ferrar (1930) Infinite integrals in the theory of Bessel functions. Quart. J. Math., Oxford Ser. 1 (1), pp. 122–145.
ⓘ

External Links:

Document, ZentralBlatt

Referenced by:

§10.32(iii).

Encodings:

BibTeX
J. M. Dixon, J. A. Tuszyński, and P. A. Clarkson (1997) From Nonlinearity to Coherence: Universal Features of Nonlinear Behaviour in Many-Body Physics. Oxford University Press, Oxford.
ⓘ

Referenced by:

Profile Peter A. Clarkson.

Encodings:

BibTeX
R. McD. Dodds and G. Wiechers (1972) Vector coupling coefficients as products of prime factors. Comput. Phys. Comm. 4 (2), pp. 268–274.
ⓘ

Notes:

Single-precision Fortran

External Links:

Document, Code

Referenced by:

4th item.

Encodings:

BibTeX
G. Doetsch (1955) Handbuch der Laplace-Transformation. Bd. II. Anwendungen der Laplace-Transformation. 1. Abteilung. Birkhäuser Verlag, Basel und Stuttgart (German).
ⓘ

External Links:

MathReview (I. I. Hirschman), ZentralBlatt

Referenced by:

§2.5(i).

Encodings:

BibTeX
D. Dominici, S. J. Johnston, and K. Jordaan (2013) Real zeros of ${}_{2}F_{1}$ hypergeometric polynomials. J. Comput. Appl. Math. 247, pp. 152–161.
ⓘ

External Links:

ISSN 0377-0427, Document, FullText, MathReview (Nasser Saad), ZentralBlatt

Referenced by:

§15.13, §15.13.

Encodings:

BibTeX
G. C. Donovan, J. S. Geronimo, and D. P. Hardin (1999) Orthogonal polynomials and the construction of piecewise polynomial smooth wavelets. SIAM J. Math. Anal. 30 (5), pp. 1029–1056.
ⓘ

External Links:

ISSN 0036-1410, Document, MathReview (Kathi Karima Selig), ZentralBlatt

Referenced by:

§16.4(iii).

Encodings:

BibTeX
B. Döring (1971) Über die Doppelnullstellen der Ableitung der Besselfunktion. Angewandte Informatik 13, pp. 402–406 (German).
ⓘ

External Links:

ZentralBlatt

Referenced by:

§10.21(i), §10.21(i), 7th item.

Encodings:

BibTeX
B. Döring (1966) Complex zeros of cylinder functions. Math. Comp. 20 (94), pp. 215–222.
ⓘ

Notes:

For a numerical error in one of the zeros see Amos (1985).

External Links:

ISSN 0025-5718, FullText, MathReview, ZentralBlatt

Referenced by:

2nd item.

Encodings:

BibTeX
E. Dorrer (1968) Algorithm 322. F-distribution. Comm. ACM 11 (2), pp. 116–117.
ⓘ

Notes:

Includes Algol program, maximum accuracy 10S. For certification see same journal 12(1969), p. 39

External Links:

ISSN 0001-0782, Document

Referenced by:

§8.28(iv).

Encodings:

BibTeX
J. Dougall (1907) On Vandermonde’s theorem, and some more general expansions. Proc. Edinburgh Math. Soc. 25, pp. 114–132.
ⓘ

External Links:

ZentralBlatt

Referenced by:

§15.4(ii).

Encodings:

BibTeX
O. Dragoun and G. Heuser (1971) A program to calculate internal conversion coefficients for all atomic shells without screening. Comput. Phys. Comm. 2 (7), pp. 427–432.
ⓘ

Notes:

Single-precision Fortran

External Links:

Document, Code

Referenced by:

1st item.

Encodings:

BibTeX
P. G. Drazin and R. S. Johnson (1993) Solitons: An Introduction. Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge.
ⓘ

External Links:

ISBN 0-521-33389-X; 0-521-33655-4, MathReview (Peter A. Clarkson), ZentralBlatt

Referenced by:

§22.19(iii), Ch.22.

Encodings:

BibTeX
P. G. Drazin and W. H. Reid (1981) Hydrodynamic Stability. Cambridge University Press, Cambridge.
ⓘ

Notes:

Cambridge Monographs on Mechanics and Applied Mathematics

External Links:

ISBN 0-521-22798-4, MathReview (Adelina Georgescu), ZentralBlatt

Referenced by:

(9.13.25), (9.13.27), (9.13.28), (9.13.29), (9.13.30), (9.13.35), (9.13.36), (9.13.37), Figure 9.13.1, Figure 9.13.1, Figure 9.13.2, Figure 9.13.2, §9.13(ii), §9.13(ii), §9.16.

Encodings:

BibTeX
K. Driver and K. Jordaan (2013) Inequalities for extreme zeros of some classical orthogonal and $q$ -orthogonal polynomials. Math. Model. Nat. Phenom. 8 (1), pp. 48–59.
ⓘ

External Links:

ISSN 0973-5348, Document, FullText, MathReview (Ana Foulquié Moreno), ZentralBlatt

Referenced by:

§18.16(ii), §18.16(iv), §18.16(ii), §18.16(iv), §18.27(iv), §18.27(iv), §18.27(v), §18.27(v).

Encodings:

BibTeX
C. F. du Toit (1993) Bessel functions $J_{n}(z)$ and $Y_{n}(z)$ of integer order and complex argument. Comput. Phys. Comm. 78 (1-2), pp. 181–189.
ⓘ

Notes:

Double-precision Pascal, maximum accuracy 7D.

External Links:

ISSN 0010-4655, Document, Code, MathReview (J. P. Singhal), ZentralBlatt

Referenced by:

2nd item.

Encodings:

BibTeX
B. A. Dubrovin (1981) Theta functions and non-linear equations. Uspekhi Mat. Nauk 36 (2(218)), pp. 11–80 (Russian).
ⓘ

Notes:

With an appendix by I. M. Krichever. In Russian. English translation: Russian Math. Surveys 36(1981), no. 2, pp. 11–92 (1982)

External Links:

ISSN 0042-1316, Document, MathReview (Alexander A. Pankov), ZentralBlatt

Referenced by:

§21.1, §21.6(ii), §21.7(i), Figure 21.9.2, Figure 21.9.2, §21.9, §21.9, Sidebar 21.SB2, Ch.21, Notations T.

Encodings:

BibTeX
B. Dubrovin and M. Mazzocco (2000) Monodromy of certain Painlevé-VI transcendents and reflection groups. Invent. Math. 141 (1), pp. 55–147.
ⓘ

External Links:

ISSN 0020-9910, Document, MathReview (Andrei A. Kapaev), ZentralBlatt

Referenced by:

§32.9(iii).

Encodings:

BibTeX
J. J. Duistermaat (1974) Oscillatory integrals, Lagrange immersions and unfolding of singularities. Comm. Pure Appl. Math. 27, pp. 207–281.
ⓘ

External Links:

MathReview (Alan Weinstein), ZentralBlatt

Referenced by:

§36.12(iii).

Encodings:

BibTeX
D. S. Dummit and R. M. Foote (1999) Abstract Algebra. 2nd edition, Prentice Hall Inc., Englewood Cliffs, N.J..
ⓘ

External Links:

ISBN 0-13-569302-0, MathReview (N. Popescu), ZentralBlatt

Referenced by:

§1.11(i), §1.11(ii), §1.11(iii).

Encodings:

BibTeX
D. Dumont and G. Viennot (1980) A combinatorial interpretation of the Seidel generation of Genocchi numbers. Ann. Discrete Math. 6, pp. 77–87.
ⓘ

Notes:

Combinatorial mathematics, optimal designs and their applications (Proc. Sympos. Combin. Math. and Optimal Design, Colorado State Univ., Fort Collins, Colo., 1978)

External Links:

MathReview (J. M. Gandhi), ZentralBlatt

Referenced by:

§24.15(i).

Encodings:

BibTeX
N. Dunford and J. T. Schwartz (1988) Linear operators. Part II. Wiley Classics Library, John Wiley & Sons, Inc., New York.
ⓘ

Notes:

Spectral theory. Selfadjoint operators in Hilbert space, With the assistance of William G. Bade and Robert G. Bartle, Reprint of the 1963 original, A Wiley-Interscience Publication

External Links:

ISBN 0-471-60847-5, MathReview Entry

Referenced by:

(1.18.68), §1.18(ix), §1.18(ix), §1.18(ix), §1.18(x).

Encodings:

BibTeX
C. F. Dunkl and Y. Xu (2001) Orthogonal Polynomials of Several Variables. Encyclopedia of Mathematics and its Applications, Vol. 81, Cambridge University Press, Cambridge.
ⓘ

External Links:

ISBN 0-521-80043-9, MathReview (Marcel de Jeu), ZentralBlatt

Referenced by:

§18.37(ii), §18.37(i).

Encodings:

BibTeX
C. F. Dunkl (1989) Differential-difference operators associated to reflection groups. Trans. Amer. Math. Soc. 311 (1), pp. 167–183.
ⓘ

External Links:

ISSN 0002-9947, Link, MathReview (W. A. Al-Salam), ZentralBlatt

Referenced by:

§18.38(iii).

Encodings:

BibTeX
C. F. Dunkl (2003) A Laguerre polynomial orthogonality and the hydrogen atom. Anal. Appl. (Singap.) 1 (2), pp. 177–188.
ⓘ

External Links:

ISSN 0219-5305, Document, Link, MathReview (E. Kreyszig), ZentralBlatt

Referenced by:

§18.39(ii), (33.14.15), Erratum (V1.0.24) for Equation (33.14.15).

Encodings:

BibTeX
C. Dunkl, M. Ismail, and R. Wong (Eds.) (2000) Special Functions. World Scientific Publishing Co., Inc., River Edge, NJ.
ⓘ

External Links:

ISBN 981-02-4393-6, Document, Link, MathReview Entry

Referenced by:

Profile Mourad E.H. Ismail.

Encodings:

BibTeX
B. I. Dunlap and B. R. Judd (1975) Novel identities for simple $n$ - $j$ symbols. J. Mathematical Phys. 16, pp. 318–319.
ⓘ

External Links:

Document, MathReview (M. J. Westwater)

Referenced by:

§34.5(vi).

Encodings:

BibTeX
G. V. Dunne and K. Rao (2000) Lamé instantons. J. High Energy Phys. 2000 (1), pp. Paper 19, 8.
ⓘ

Notes:

(electronic only, article id. JHEP01(2000)019, 8 pp.).

External Links:

ISSN 1029-8479, Document, MathReview, ZentralBlatt

Referenced by:

§22.11.

Encodings:

BibTeX
T. M. Dunster, D. A. Lutz, and R. Schäfke (1993) Convergent Liouville-Green expansions for second-order linear differential equations, with an application to Bessel functions. Proc. Roy. Soc. London Ser. A 440, pp. 37–54.
ⓘ

External Links:

ISSN 0962-8444, FullText, MathReview (W. Balser), ZentralBlatt

Referenced by:

§10.41(iii), §2.8(i).

Encodings:

BibTeX
T. M. Dunster, R. B. Paris, and S. Cang (1998) On the high-order coefficients in the uniform asymptotic expansion for the incomplete gamma function. Methods Appl. Anal. 5 (3), pp. 223–247.
ⓘ

External Links:

ISSN 1073-2772, Pdf, MathReview (John G. Stalker), ZentralBlatt

Referenced by:

§8.12.

Encodings:

BibTeX
T. M. Dunster (1986) Uniform asymptotic expansions for prolate spheroidal functions with large parameters. SIAM J. Math. Anal. 17 (6), pp. 1495–1524.
ⓘ

External Links:

ISSN 0036-1410, Document, MathReview (R. K. Gupta), ZentralBlatt

Referenced by:

§30.9(i).

Encodings:

BibTeX
T. M. Dunster (1989) Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions. SIAM J. Math. Anal. 20 (3), pp. 744–760.
ⓘ

Notes:

(This reference has several typographical errors.)

External Links:

ISSN 0036-1410, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§13.21(ii), §13.21(iii), §13.21(iv).

Encodings:

BibTeX
T. M. Dunster (1990a) Bessel functions of purely imaginary order, with an application to second-order linear differential equations having a large parameter. SIAM J. Math. Anal. 21 (4), pp. 995–1018.
ⓘ

Notes:

Errata: In eq. (2.8) replace $(x^{2}/4)^{2}$ by $(x^{2}/4)^{s}$ . In eq. (4.2) $\phi(\zeta)$ should be replaced by $\psi(\zeta)$ . In the second line of eq. (4.7) insert an external factor $e^{-2\pi ij/3}$ and change the upper limit of the sum to $n-1$ . In eq. (4.15) the factor $\zeta$ is missing from the arguments of the functions Bi_ν and Bi’_ν.

External Links:

ISSN 0036-1410, Document, MathReview (A. de Castro Brzezicki), ZentralBlatt

Referenced by:

§10.24, §10.45, §2.8(iv).

Encodings:

BibTeX
T. M. Dunster (1990b) Uniform asymptotic solutions of second-order linear differential equations having a double pole with complex exponent and a coalescing turning point. SIAM J. Math. Anal. 21 (6), pp. 1594–1618.
ⓘ

External Links:

ISSN 0036-1410, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§14.26, §2.8(vi).

Encodings:

BibTeX
T. M. Dunster (1991) Conical functions with one or both parameters large. Proc. Roy. Soc. Edinburgh Sect. A 119 (3-4), pp. 311–327.
ⓘ

External Links:

ISSN 0308-2105, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§14.20(i), §14.20(ix), §14.20(ix), §14.20(viii), §14.23.

Encodings:

BibTeX
T. M. Dunster (1992) Uniform asymptotic expansions for oblate spheroidal functions I: Positive separation parameter $\lambda$ . Proc. Roy. Soc. Edinburgh Sect. A 121 (3-4), pp. 303–320.
ⓘ

External Links:

ISSN 0308-2105, MathReview (Archibald D. MacGillivray), ZentralBlatt

Referenced by:

§30.9(ii).

Encodings:

BibTeX
T. M. Dunster (1994a) Uniform asymptotic approximation of Mathieu functions. Methods Appl. Anal. 1 (2), pp. 143–168.
ⓘ

External Links:

ISSN 1073-2772, Pdf, MathReview (J. M. H. Peters), ZentralBlatt

Referenced by:

§28.8(iv).

Encodings:

BibTeX
T. M. Dunster (1994b) Uniform asymptotic solutions of second-order linear differential equations having a simple pole and a coalescing turning point in the complex plane. SIAM J. Math. Anal. 25 (2), pp. 322–353.
ⓘ

External Links:

ISSN 0036-1410, Document, MathReview (H. C. Howard), ZentralBlatt

Referenced by:

§2.8(vi).

Encodings:

BibTeX
T. M. Dunster (1995) Uniform asymptotic expansions for oblate spheroidal functions II: Negative separation parameter $\lambda$ . Proc. Roy. Soc. Edinburgh Sect. A 125 (4), pp. 719–737.
ⓘ

External Links:

ISSN 0308-2105, MathReview (Archibald D. MacGillivray), ZentralBlatt

Referenced by:

§30.9(ii).

Encodings:

BibTeX
T. M. Dunster (1996a) Asymptotic solutions of second-order linear differential equations having almost coalescent turning points, with an application to the incomplete gamma function. Proc. Roy. Soc. London Ser. A 452, pp. 1331–1349.
ⓘ

External Links:

ISSN 0962-8444, FullText, MathReview, ZentralBlatt

Referenced by:

§2.8(vi), §8.12, §8.12.

Encodings:

BibTeX
T. M. Dunster (1996b) Asymptotics of the generalized exponential integral, and error bounds in the uniform asymptotic smoothing of its Stokes discontinuities. Proc. Roy. Soc. London Ser. A 452, pp. 1351–1367.
ⓘ

External Links:

ISSN 0962-8444, FullText, MathReview (Alexander Tovbis), ZentralBlatt

Referenced by:

§2.11(iii), §8.20(ii).

Encodings:

BibTeX
T. M. Dunster (1996c) Error bounds for exponentially improved asymptotic solutions of ordinary differential equations having irregular singularities of rank one. Methods Appl. Anal. 3 (1), pp. 109–134.
ⓘ

External Links:

ISSN 1073-2772, Pdf, MathReview (Roderick Wong), ZentralBlatt

Referenced by:

§2.11(v).

Encodings:

BibTeX
T. M. Dunster (1997) Error analysis in a uniform asymptotic expansion for the generalised exponential integral. J. Comput. Appl. Math. 80 (1), pp. 127–161.
ⓘ

External Links:

ISSN 0377-0427, Document, MathReview (Eberhard Wagner), ZentralBlatt

Referenced by:

§2.11(iii), §8.20(ii).

Encodings:

BibTeX
T. M. Dunster (1999) Asymptotic approximations for the Jacobi and ultraspherical polynomials, and related functions. Methods Appl. Anal. 6 (3), pp. 21–56.
ⓘ

External Links:

ISSN 1073-2772, Pdf, MathReview (Walter Van Assche), ZentralBlatt

Referenced by:

§15.12(iii), §18.15(i), §18.15(vi).

Encodings:

BibTeX
T. M. Dunster (2001a) Convergent expansions for solutions of linear ordinary differential equations having a simple turning point, with an application to Bessel functions. Stud. Appl. Math. 107 (3), pp. 293–323.
ⓘ

External Links:

ISSN 0022-2526, Document, MathReview, ZentralBlatt

Referenced by:

§10.20(ii), §2.8(i).

Encodings:

BibTeX
T. M. Dunster (2001b) Uniform asymptotic expansions for Charlier polynomials. J. Approx. Theory 112 (1), pp. 93–133.
ⓘ

External Links:

ISSN 0021-9045, Document, MathReview (Eberhard Wagner), ZentralBlatt

Referenced by:

§18.24.

Encodings:

BibTeX
T. M. Dunster (2001c) Uniform asymptotic expansions for the reverse generalized Bessel polynomials, and related functions. SIAM J. Math. Anal. 32 (5), pp. 987–1013.
ⓘ

External Links:

ISSN 0036-1410, Document, MathReview (Hasan Taşeli), ZentralBlatt

Referenced by:

§10.49(ii), §18.34(iii).

Encodings:

BibTeX
T. M. Dunster (2003a) Uniform asymptotic approximations for the Whittaker functions $M_{\kappa,i\mu}(z)$ and $W_{\kappa,i\mu}(z)$ . Anal. Appl. (Singap.) 1 (2), pp. 199–212.
ⓘ

External Links:

ISSN 0219-5305, Document, MathReview (Hasan Taşeli), ZentralBlatt

Referenced by:

§13.20(v).

Encodings:

BibTeX
T. M. Dunster (2003b) Uniform asymptotic expansions for associated Legendre functions of large order. Proc. Roy. Soc. Edinburgh Sect. A 133 (4), pp. 807–827.
ⓘ

External Links:

ISSN 0308-2105, Document, MathReview, ZentralBlatt

Referenced by:

§14.15(i), §14.15(i), §14.15(ii), §14.15(ii), §14.26.

Encodings:

BibTeX
T. M. Dunster (2004) Convergent expansions for solutions of linear ordinary differential equations having a simple pole, with an application to associated Legendre functions. Stud. Appl. Math. 113 (3), pp. 245–270.
ⓘ

External Links:

ISSN 0022-2526, Document, MathReview (Wolfgang Bühring), ZentralBlatt

Referenced by:

§14.15(iii), §2.8(i).

Encodings:

BibTeX
T. M. Dunster (2006) Uniform asymptotic approximations for incomplete Riemann zeta functions. J. Comput. Appl. Math. 190 (1-2), pp. 339–353.
ⓘ

External Links:

ISSN 0377-0427, Document, MathReview Entry, ZentralBlatt

Referenced by:

§8.22(ii).

Encodings:

BibTeX
T. M. Dunster (2013) Conical functions of purely imaginary order and argument. Proc. Roy. Soc. Edinburgh Sect. A 143 (5), pp. 929–955.
ⓘ

External Links:

ISSN 0308-2105, Document, Link, MathReview (Eugenia N. Petropoulou), ZentralBlatt

Referenced by:

§14.20(ix), §14.20(ix).

Encodings:

BibTeX
T. M. Dunster (2014) Olver’s error bound methods applied to linear ordinary differential equations having a simple turning point. Anal. Appl. (Singap.) 12 (4), pp. 385–402.
ⓘ

External Links:

ISSN 0219-5305, Document, Link, MathReview (Thomas Mbah Acho), ZentralBlatt

Referenced by:

5th item, §14.32.

Encodings:

BibTeX
A. J. Durán and F. A. Grünbaum (2005) A survey on orthogonal matrix polynomials satisfying second order differential equations. J. Comput. Appl. Math. 178 (1-2), pp. 169–190.
ⓘ

External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§18.36(iv).

Encodings:

BibTeX
A. J. Durán (1993) Functions with given moments and weight functions for orthogonal polynomials. Rocky Mountain J. Math. 23, pp. 87–104.
ⓘ

External Links:

ISSN 0035-7596, MathReview (Olav Njåstad), ZentralBlatt

Referenced by:

§18.34(ii).

Encodings:

BibTeX
L. Durand (1975) Nicholson-type Integrals for Products of Gegenbauer Functions and Related Topics. In Theory and Application of Special Functions (Proc. Advanced Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1975), R. A. Askey (Ed.), pp. 353–374. Math. Res. Center, Univ. Wisconsin, Publ. No. 35.
ⓘ

External Links:

MathReview (K. M. Saksena), ZentralBlatt

Referenced by:

(12.12.4), §12.12, §18.17(iii), §18.17(iii).

Encodings:

BibTeX
L. Durand (1978) Product formulas and Nicholson-type integrals for Jacobi functions. I. Summary of results. SIAM J. Math. Anal. 9 (1), pp. 76–86.
ⓘ

External Links:

Document, MathReview (R. C. Varma), ZentralBlatt

Referenced by:

§18.17(iii).

Encodings:

BibTeX
P. L. Duren (1991) The Legendre Relation for Elliptic Integrals. In Paul Halmos: Celebrating 50 Years of Mathematics, J. H. Ewing and F. W. Gehring (Eds.), pp. 305–315.
ⓘ

External Links:

ISBN 0-387-97509-8, MathReview (J. M. H. Peters), ZentralBlatt

Referenced by:

§19.7(i).

Encodings:

BibTeX
J. Dutka (1981) The incomplete beta function—a historical profile. Arch. Hist. Exact Sci. 24 (1), pp. 11–29.
ⓘ

External Links:

ISSN 0003-9519, MathReview (Willard Parker), ZentralBlatt

Referenced by:

§8.17(i).

Encodings:

BibTeX
R. Dutt, A. Khare, and U. P. Sukhatme (1988) Supersymmetry, shape invariance, and exactly solvable potentials. Amer. J. Phys. 56, pp. 163–168.
ⓘ

Referenced by:

§18.38(iii).

Encodings:

BibTeX
A. Dzieciol, S. Yngve, and P. O. Fröman (1999) Coulomb wave functions with complex values of the variable and the parameters. J. Math. Phys. 40 (12), pp. 6145–6166.
ⓘ

External Links:

ISSN 0022-2488, Document, MathReview (Raj Wilson), ZentralBlatt

Referenced by:

§33.13.

Encodings:

BibTeX

Site Privacy Accessibility Privacy Program Copyrights Vulnerability Disclosure No Fear Act Policy FOIA Environmental Policy Scientific Integrity Information Quality Standards Commerce.gov Science.gov USA.gov