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Generating functions of Legendre polynomials: a tribute to Fred Brafman. (English) Zbl 1282.33015
This is a reprint of an article (with the same title and content) by these authors, that appeared in [ibid. 164, No. 4, 488–503 (2012; Zbl 1242.33018)].

33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
11B83 Special sequences and polynomials
65Q30 Numerical aspects of recurrence relations
Zbl 1242.33018
Full Text: DOI
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[2] Bailey, W. N., (Generalized Hypergeometric Series, Cambridge Math. Tracts, vol. 32, (1935), Cambridge Univ. Press Cambridge), second reprinted ed., Stechert-Hafner, New York, London, 1964
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[4] Borwein, J. M.; Straub, A.; Wan, J.; Zudilin, W., With an appendix by D. Zagier, densities of short uniform random walks, Canad. J. Math., 64, 961-990, (2012) · Zbl 1296.33011
[5] Brafman, F., Generating functions of Jacobi and related polynomials, Proc. Amer. Math. Soc., 2, 942-949, (1951) · Zbl 0044.07602
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[9] H.H. Chan, J. Wan, W. Zudilin, Legendre polynomials and Ramanujan-type series for \(1 / \pi\), Israel J. Math. (2013) http://dx.doi.org/10.1007/s11856-012-0081-5 (in press). · Zbl 1357.11123
[10] Clausen, T., Ueber die Fälle wenn die reihe \(y = 1 + \frac{\alpha \beta}{1 \cdot \gamma} x + \cdots\) ein quadrat von der form \(y = 1 + \frac{\alpha^\prime \beta^\prime \gamma^\prime}{1 \cdot \delta^\prime \epsilon^\prime} x + \cdots\) hat, J. Math., 3, 89-95, (1828)
[11] Ramanujan, S., Modular equations and approximations to \(\pi\), Q. J. Math. (Oxford), 45, 350-372, (1914) · JFM 45.1249.01
[12] Srivastava, H. M., An equivalence theorem on generating functions, Proc. Amer. Math. Soc., 52, 159-165, (1975) · Zbl 0311.33014
[13] Z.-W. Sun, List of conjectural series for powers of \(\pi\) and other constants, Preprint (2011). arXiv:1102.5649v21 [math.CA].
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