L'Autore prova che alcuni risultati sulle funzioni generatrici ottenuti da O. Shanker [«J. Australian Math. Soc.», 15 (1973), 389-392] sono equivalenti ad altri noti risultati. Si provano alcune generalizzazioni e la loro applicazione a famiglie polinomiali di Bessel, Brafman, Gegenbauer, Hermite, Jacobi e Laguerre.
@article{RLINA_1977_8_63_5_328_0,
author = {Hari M. Srivastava},
title = {A note on certain generating functions for the classical polynomials},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
volume = {62},
year = {1977},
pages = {328-333},
zbl = {0362.33005},
mrnumber = {0548596},
language = {en},
url = {http://dml.mathdoc.fr/item/RLINA_1977_8_63_5_328_0}
}
Srivastava, Hari M. A note on certain generating functions for the classical polynomials. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 62 (1977) pp. 328-333. http://gdmltest.u-ga.fr/item/RLINA_1977_8_63_5_328_0/
[1] (1957) - Some generating functions for Laguerre and Hermite polynomials, «Canad. J. Math.», 9, 180-187. | MR 85363 | Zbl 0078.25702
[2] (1969) - New generating functions for classical polynomials, «Proc. Amer. Math. Soc.», 21, 263-268. | MR 236438 | Zbl 0175.07302
[3] (1968) - Some generating functions for Laguerre polynomials, «Duke Math. J.», 35, 825-827. | MR 240351 | Zbl 0167.35202
[4] (1956) - Some generalizations of Vandermonde's convolution, «Amer. Math. Monthly», 63, 84-91. | MR 75170 | Zbl 0072.00702
[5] and (1962) - Operational formulas connected with two generalizations of Hermite polynomials, «Duke Math. J.», 29, 51-63. | MR 132853 | Zbl 0108.06504
[6] and (1949) - A new class of orthogonal polynomials: the Bessel polynomials, «Trans. Amer. Math. Soc.», 65, 100-115. | MR 28473 | Zbl 0031.29701
[7] and (1972) - Problems and Theorems in Analysis, Vol. I (Translated from the German by D. Aeppli), Springer-Verlag, New York, Heidelberg and Berlin. | MR 344042
[8] (1968) — Combinatorial Identities, John Wiley and Sons, Inc., New York, London and Sydney. | MR 231725 | Zbl 0194.00502
[9] (1973) - On generating functions for classical polynomials, «J. Austral. Math. Soc.», 15, 389-392. | MR 326026 | Zbl 0276.33025
[10] (1971) - A class of generating functions for generalized hypergeometric polynomials, «J. Math. Anal. Appl.», 35, 230-235. | MR 277776 | Zbl 0212.40901
[11] and (1975) - Some polynomials defined by generating relations, «Trans. Amer. Math. Soc.», 205, 360-370; see also Addendum, ibid., 226 (1977), 393-394. | MR 430365
[12] (1970) — A new class of generating functions for hypergeometric polynomials, «Proc. Amer. Math. Soc.», 25, 405-412. | MR 264123 | Zbl 0192.41501