Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-24T13:16:32.012Z Has data issue: false hasContentIssue false
  • English
  • Français

Generalized Neumann expansions involving hypergeometric functions

Published online by Cambridge University Press:  24 October 2008

H. M. Srivastava
H. M. Srivastava
Affiliation:
Department of Mathematics, The University, Jodhpur, India
Get access Rights & Permissions [Opens in a new window]

Extract

1. Making use of the familiar abbreviation

let us adopt a contracted notation for the generalized hypergeometric function AFB[x] and write

where (a) denotes the sequence of parameters

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 2 , April 1967 , pp. 425 - 429
Copyright
Copyright © Cambridge Philosophical Society 1967

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Appell, P. and Kampé de Fériet, J.Fonctions hypergéométriques et hypersphériques. Polynomes d'Hermite (Gauthier-Villars; Paris, 1926).Google Scholar
(2)Bailey, W. N.Some expansions in Bessel functions involving Appell's function F 4. Quart. J. Math. Oxford Series 6 (1935), 233–238.CrossRefGoogle Scholar
(3)Burchnall, J. L. and Chaundy, T. W.Expansions of Appell's double hypergeometric functions. II. Quart. J. Math. Oxford Series 12 (1941), 112–128.CrossRefGoogle Scholar
(4)Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.Higher transcendental functions. Vol. II (McGraw-Hill; New York, 1953).Google Scholar
(5)Lauricella, G.Sulle funzioni ipergeometriche a piu variabili. Rend. Circ. Mat. Palermo, 7 (1893), 111–158.CrossRefGoogle Scholar
(6)Slater, L. J.Expansions of generalized Whittaker functions. Proc. Cambridge Philos. Soc. 50 (1954), 628–631.CrossRefGoogle Scholar
(7)Slater, L. J.Confluent hypergeometric functions (Cambridge, 1960).Google Scholar
(8)Srivastava, H. M.Some expansions of generalized Whittaker functions. Proc. Cambridge Philos. Soc. 61 (1965), 895–896.CrossRefGoogle Scholar
(9)Srivastava, H. M.Some expansions in products of hypergeometric functions. Proc. Cambridge Philos. Soc. 62 (1966), 245–247.CrossRefGoogle Scholar
(10)Watson, G. N.Theory of Bessel functions (Cambridge, 1944).Google Scholar