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Notes:
English translation: Soviet Math. Dokl. 31(1985), no. 1,
pp. 45–47
M. J. Ablowitz and P. A. Clarkson (1991)Solitons, Nonlinear Evolution Equations and Inverse Scattering.
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Corrections appeared in later printings up to the 10th Printing, December, 1972. Reproductions by other publishers, in whole or in part, have been available since 1965.
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Notes:
SPHEREPACK 2.0 is a collection of Fortran programs that facilitates
computer modeling of geophysical processes. Accurate solutions are
obtained via the spectral method that uses both scalar and vector
spherical harmonic transforms. The package also contains utility programs
for computing the associated Legendre functions. SPHEREPACK 3.1 was
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A third edition was published in 1978 by McGraw-Hill, New York.
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Notes:
Translated from the second Russian edition by H. H. McFaden
N. I. Akhiezer (2021)The classical moment problem and some related questions in analysis.
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Reprint of the 1965 edition [ 0184042],
Translated by N. Kemmer,
With a foreword by H. J. Landau
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Includes algorithms for Lerch’s transcendent. C and Mathematica codes by Aksenov and Jentschura are available.
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D. E. Amos (1985)A subroutine package for Bessel functions of a complex argument and nonnegative order.
Technical ReportTechnical Report SAND85-1018, Sandia National Laboratories, Albuquerque, NM.
D. E. Amos (1986)Algorithm 644: A portable package for Bessel functions of a complex argument and nonnegative order.
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ⓘ
Notes:
Single and double precision, maximum accuracy 18S.
D. E. Amos (1990)Algorithm 683: A portable FORTRAN subroutine for exponential integrals of a complex argument.
ACM Trans. Math. Software16 (2), pp. 178–182.
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Notes:
Double- and single-precision Fortran, maximum accuracy 18S or 14S.
G. D. Anderson, S.-L. Qiu, M. K. Vamanamurthy, and M. Vuorinen (2000)Generalized elliptic integrals and modular equations.
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G. D. Anderson, M. K. Vamanamurthy, and M. Vuorinen (1992a)Functional inequalities for hypergeometric functions and complete elliptic integrals.
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G. D. Anderson, M. K. Vamanamurthy, and M. Vuorinen (1992b)Hypergeometric Functions and Elliptic Integrals.
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G. D. Anderson, M. K. Vamanamurthy, and M. K. Vuorinen (1997)Conformal Invariants, Inequalities, and Quasiconformal Maps.
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ⓘ
Notes:
With PC diskette,
a Wiley-Interscience Publication
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Reprinted by Cambridge University Press, Cambridge, 1998.
G. E. Andrews (1986)-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics, and Computer Algebra.
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in Science and Technology, Springer-Verlag.
An extended-precision C code for special functions. The library uses arbitrary-precision
ball arithmetic. Ball arithmetic is an efficient technique for performing numerical computations
with automatic and rigorous tracking of error bounds. Arb is designed with computer algebra
and computational number theory in mind, extending the principles behind FLINT to the
domain of real and complex numbers.
R. W. B. Ardill and K. J. M. Moriarty (1978)Spherical Bessel functions and of integer order and real argument.
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Funkcional. Anal. i Priložen.6 (4), pp. 3–25 (Russian).
ⓘ
Notes:
In Russian. English translation: Functional Anal. Appl.,
6(1973), pp. 254–272.
V. I. Arnol’d (1974)Normal forms of functions in the neighborhood of degenerate critical points.
Uspehi Mat. Nauk29 (2(176)), pp. 11–49 (Russian).
ⓘ
Notes:
Collection of articles dedicated to the memory of Ivan
Georgievič Petrovskiĭ (1901–1973), I. In Russian.
English translation: Russian Math. Surveys, 29(1974),
no. 2, pp. 10–50.
F. M. Arscott (1964b)Periodic Differential Equations. An Introduction to Mathieu, Lamé, and Allied Functions.
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U. M. Ascher and L. R. Petzold (1998)Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations.
Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
R. A. Askey, T. H. Koornwinder, and W. Schempp (Eds.) (1984)Special Functions: Group Theoretical Aspects and Applications.
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ⓘ
Notes:
Reprinted by Kluwer Academic Publishers, Boston, 2001.
R. Askey, T. H. Koornwinder, and M. Rahman (1986)An integral of products of ultraspherical functions and a -extension.
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R. Askey (1974)Jacobi polynomials. I. New proofs of Koornwinder’s Laplace type integral representation and Bateman’s bilinear sum.
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R. Askey (1975b)Orthogonal Polynomials and Special Functions.
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