IJPAM: Volume 85, No. 5 (2013)

ON GENERATING FUNCTIONS OF
MODIFIED GEGENBAUER POLYNOMIALS

S. Alam1, A.K. Chongdar2
Department of Mathematics
Bengal Engineering and Science University
Shibpur, P.O. Botanic Garden, Howrah, 711 103, INDIA


Abstract. In this article, we have obtained some novel theorems on generating functions (both bilateral and mixed trilateral) of modified Gegenbauer polynomials by introducing a partial differential operator obtained by single interpretation to the index of the polynomial under consideration in Weisner's group-theoretic method [2]. Furthermore, we have shown that the results obtained by Das and Chatterjea [1], while investigating some problems on bilateral and mixed trilateral generating functions of Gegenbauer polynomials by using the operator obtained by double interpretations to the index and the parameter simultaneously in Weisner's method, can be easily obtained from our results obtained in this paper. Some applications of our results are also discussed.

Received: November 1, 2008

AMS Subject Classification: 33C47

Key Words and Phrases: Gegenbauer polynomials, generating functions, special functions

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DOI: 10.12732/ijpam.v85i5.1 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 85
Issue: 5