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Expansion of the hypergeometric function in series of confluent ones and application to the Jacobi polynomials

โœ Scribed by Francesco G. Tricomi

Book ID
112783208
Publisher
European Mathematical Society
Year
1951
Tongue
English
Weight
424 KB
Volume
25
Category
Article
ISSN
0010-2571

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๐Ÿ“œ SIMILAR VOLUMES

On the expansion of confluent hypergeome
On the expansion of confluent hypergeometric functions in terms of Bessel functions
โœ N.M. Temme ๐Ÿ“‚ Article ๐Ÿ“… 1981 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 427 KB

For the confluent hypergeometric functions U (a, b, z) and M (a, b, z) asymptotic expansions are given for a -~ ,o. The expansions contain modified Bessel functions. For real values of the parameters rigorous error bounds are given.

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An asymptotic expansion of the confluent hypergeometric function U(a,b,x) for large positive 2a-b is given in terms of modified Bessel functions multiplied by Buchholz polynomials, a family of double polynomials in the variables b and x with rational coefficients.

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โœ Whei-Ching C. Chan; Kung-Yu Chen; H.M. Srivastava ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 1018 KB

For a certain class of generalized hypergcometric polynomials, the authors first derive a general theorem on bilinear, bilateral, and mixed multilateral generating functions and then apply these generating functions in order to deduce the corresponding results for the classical Jacobi and Laguerre p