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A generalization of André-Jeannin’s symmetric identity


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[1] W. A. Al-Salam and M. E. H. Ismail, Orthogonal polynomials associated with the Rogers-Ramanujan continued fraction, Pacific J. Math., 104 (1983) 269–283.10.2140/pjm.1983.104.269Search in Google Scholar

[2] R. André-Jeannin, Summation of reciprocals in certain second-order recurring sequences, Fibonacci Quart., 35 (1997) 68–74.Search in Google Scholar

[3] K. S. Briggs, D. P. Little and J. A. Sellers, Tiling proofs of various q-Pell identities via tilings, Ann. Comb., 14 (2010) 407–418.10.1007/s00026-011-0067-8Search in Google Scholar

[4] L. Carlitz, Fibonacci notes 3: q-Fibonacci numbers, Fibonacci Quart., 12 (1974) 317–322.Search in Google Scholar

[5] L. Carlitz, Fibonacci notes 4: q-Fibonacci polynomials, Fibonacci Quart., 13 (1975) 97–102.Search in Google Scholar

[6] I. J. Good, A symmetry property of alternating sums of products of reciprocals, Fibonacci Quart., 32 (1994) 284–287.Search in Google Scholar

[7] A. M. Goyt and B. E. Sagan, Set partition statistics and q-Fibonacci numbers, European J. Combin., 30 (2009) 230–245.10.1016/j.ejc.2008.01.015Search in Google Scholar

[8] A. F. Horadam, Basic properties of a certain generalized sequence of numbers, Fibonacci Quart., 3 (1965) 161–176.Search in Google Scholar

[9] A. F. Horadam, Generating functions for powers of a certain generalized sequence of numbers, Duke Math. J., 32 (1965) 437–446.10.1215/S0012-7094-65-03244-8Search in Google Scholar

[10] M. E. H. Ismail, H. Prodinger and D. Stanton, Schur’s determinants and partition theorems, Sém. Lothar. Combin., B44a (2000) 10 pp.Search in Google Scholar

[11] M. E. H. Ismail and D. Stanton, Ramanujan continued fractions via orthogonal polynomials, Adv. Math., 203 (2006) 170–193.10.1016/j.aim.2005.04.006Search in Google Scholar

[12] T. Mansour and M. Shattuck, Restricted partitions and q-Pell numbers, Cent. Eur. J. Math., 9 (2011) 346–355.10.2478/s11533-011-0002-6Search in Google Scholar

[13] A. M. Morgan-Voyce, Ladder network analysis using Fibonacci numbers, IRE Transactions on Circuit Theory, 6.3 (1959) 321–322.10.1109/TCT.1959.1086564Search in Google Scholar

[14] E. Munarini, Generalized q-Fibonacci numbers, Fibonacci Quart., 43 (2005) 234–242.Search in Google Scholar

[15] H. Pan, Arithmetic properties of q-Fibonacci numbers and q-Pell numbers, Discrete Math., 306 (2006) 2118–2127.10.1016/j.disc.2006.03.067Search in Google Scholar

[16] J. O. Santos and A. V. Sills, q-Pell sequences and two identities of V. A. Lebesgue, Discrete Math., 257 (2002) 125–142.10.1016/S0012-365X(01)00475-7Search in Google Scholar

[17] I. Schur, Gesmmelte Abhandungen, Vol. 2, Springer-Verlag, Berlin, 1973, pp. 117–136.Search in Google Scholar

[18] N. J. A. Sloane, On-Line Encyclopedia of Integer Sequences, published electronically at http://oeis.org/.Search in Google Scholar

[19] M. N. S. Swamy, Properties of the polynomials defined by Morgan-Voyce, Fibonacci Quart., 4 (1966) 73–81.Search in Google Scholar

[20] M. N. S. Swamy, Further properties of Morgan-Voyce polynomials, Fibonacci Quart., 6 (1968) 167–175.Search in Google Scholar