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Generating functions play an important role in the investigation of various useful properties of the sequences which they generate. Exton \cite{Exto-93} presented a very general double generating relation involving products of two Laguerre polynomials. Motivated essentially by Exton's derivation \cite{Exto-93}, the authors aim to show how one can obtain nineteen new generating relations associated with products of two Laguerre polynomials in the form of a single result. We also consider some interesting and potentially useful special cases of our main findings.
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참고문헌 (20)
참고문헌 신청
A. Erd´elyi / 1953 / Higher Transcendental Functions. Vol. I / McGraw-Hill Book Company
E. D. Rainville / 1960 / Special Functions / Macmillan Company
H. Exton / 1976 / Multiple Hypergeometric Functions and Applications / Halsted Press
H. Exton / 1993 / New generating relations for products of two Laguerre polynomials / Indian J. Pure Appl. Math 24 (6) : 401 ~ 408
H. M. Srivastava / 1976 / An integral representation for the product of two Jacobi polynomials / J. London Math. Soc 12 (4) : 419 ~ 425
E. D. Rainville / 1960 / Special Functions / Macmillan Company
H. Exton / 1976 / Multiple Hypergeometric Functions and Applications / Halsted Press
H. Exton / 1993 / New generating relations for products of two Laguerre polynomials / Indian J. Pure Appl. Math 24 (6) : 401 ~ 408
H. M. Srivastava / 1976 / An integral representation for the product of two Jacobi polynomials / J. London Math. Soc 12 (4) : 419 ~ 425
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