Hostname: page-component-5c6d5d7d68-7tdvq Total loading time: 0 Render date: 2024-08-30T19:27:26.525Z Has data issue: false hasContentIssue false
  • English
  • Français

On a summation formula for the Appell function F2

Published online by Cambridge University Press:  24 October 2008

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

Extract

1. In the course of a systematic analysis of certain problems in quantum mechanics it has been observed that their exact solutions can be expressed in terms of the Appell function F2 defined by means of (see e.g. (8), p. 211)

where, as usual,

and for convergence of the double series,

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 4 , October 1967 , pp. 1087 - 1089
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. et Kampé de, Fériet J.Fonctions hypergéométriques et hypersphériques (Gauthier–Villars; Paris, 1926).Google Scholar
(2)Bailey, W. N.Generalized hypergeometric series (Cambridge, 1935).Google Scholar
(3)Bhatt, R. C.A summation formula for Appell's function F 2. Israel J. Math. 3 (1965), 87–88.Google Scholar
(4)Erdélyi, A.Transformations of hypergeometric functions of two variables. Proc. Roy. Soc. Edinburgh. Sect. A 62 (1948), 378–385.Google Scholar
(5)Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.Higher transcendental functions, vol. II (McGraw-Hill; New York, 1953).Google Scholar
(6)Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.Tables of integral transforms, vol. II (McGraw-Hill; New York, 1954).Google Scholar
(7)Slater, L. J.Confluent hypergeometric functions (Cambridge, 1960).Google Scholar
(8)Slater, L. J.Generalized hypergeometric functions (Cambridge, 1966).Google Scholar