Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-19T13:34:48.106Z Has data issue: false hasContentIssue false

A new generating function for Jacobi polynomials

Published online by Cambridge University Press:  24 October 2008

B. L. Sharma
Affiliation:
Department of Mathematics, Regional Centre, Simla, India

Extract

In this paper we give a new generating function for the Jacobi polynomials. The result obtained is of general character and includes as particular cases some of the results given earlier by Carlitz(2), Salam(1), Manocha and Sharma (3,4).

Type
Research Article
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)Al-Salam, W. A.Operational representations for the Laguerre and other polynomials. Duke Math. J. 31 (1964), 127142.Google Scholar
(2)Carlitz, L.A bilinear generating function for the Jacobi polynomials. Boll. Un. Mat. Ital. 18 (1963), 8789.Google Scholar
(3)Manocha, H. L. and Sharma, B. L.Infinite series of hypergeometric functions. Annales Soc. Sci. Bruxelles, Sér. I 80 (1966), 7386.Google Scholar
(4)Manocha, H. L. and Sharma, B. L.Some formulae for Jacobi polynomials. Proc. Cambridge Philos. Soc. 62 (1966), 459462.Google Scholar
(5)Appell, P. and Kampé, J. de Feriet. Functions hypergéometriques et hypersphériques. Polynômes d'Hermite (Gauthier-Villars, Paris, 1926).Google Scholar
(6)Pandey, R. C.On certain hypergeometric transformations. J. Math. Mech. 12 (1963), 113118.Google Scholar
(7)Rainville, E. D.Special functions (1965).Google Scholar
(8)Saran, S.Hypergeometric functions of three variables. Ganita 5 (1954), 8390.Google Scholar
(9)Szego, G.Orthogonal polynomials (1939).Google Scholar