Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-29T19:00:13.707Z Has data issue: false hasContentIssue false
  • English
  • Français

Some combinatorial series identities

Published online by Cambridge University Press:  24 October 2008

H. M. Srivastava  and
R. K. Raina
H. M. Srivastava
Affiliation:
Department of Mathematics, University of Victoria, Victoria, British Columbia V8W 2Y2, Canada
R. K. Raina
Affiliation:
Department of Mathematics, S.K.N. Agriculture College, University of Udaipur, Jobmer-303329, Rajasthan, India
Get access Rights & Permissions [Opens in a new window]

Abstract

While expanding upon the work of H. M. Srivastava [6] on generalizations of an interesting identity of Carlson, R. G. Buschman and H. M. Srivastava [2] proved a number of double-series identities and listed various cases of reducibility of certain hypergeometric series in two variables (cf. [1], p. 150, equation (29)). The object of the present paper is to derive three new classes of combinatorial series identities (contained in Theorems 1, 2 and 3 below) which unify and extend the results of these earlier papers ([2], [6]). A multiple-series analogue of one of the combinatorial series identities presented here is also recorded.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 96 , Issue 1 , July 1984 , pp. 9 - 13
Copyright
Copyright © Cambridge Philosophical Society 1984

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

[1] Appell, P. et de Fériet, J. Kampé. Fonctions hypergéométriques et hypersphériques; poly-nômes d'Hermite (Gauthier-Villars, 1926).Google Scholar
[2] Buschman, R. G. and Srivastava, H. M.. Series identities and reducibility of Kampé de Fériet functions. Math. Proc. Cambridge Philos. Soc. 91 (1982), 435–440.CrossRefGoogle Scholar
[3] Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.. Higher Transcendental Functions, vol. I (McGraw-Hill, 1953).Google Scholar
[4] Gould, H. W.. Combinatorial Identities (Morgantown, 1972).Google Scholar
[5] Riordan, J.. Combinatorial Identities (John Wiley, 1968).Google Scholar
[6] Srivastava, H. M.. Some generalizations of Carlson's identity. Boll. Un. Mat. Ital. (5), 18A (1981), 138–143.Google Scholar