Mathematics and Statistics Vol. 2(4), pp. 172 - 178
DOI: 10.13189/ms.2014.020403
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Some Generating Functions of Modified Gegenbauer Polynomials by Lie Algebraic Method

K.P. Samanta ¹, B. C. Chandra ^2,*, C.S.Bera ^3
1 Department of Mathematics, Bengal Engineering and Science University, Shibpur P.O. Botanic Garden, Howrah - 711 103, India
² Sree Vidyaniketan; 9A, J. M. Avenue, Kolkata - 700006, W.B, India
³ Department of Mathematics, Bagnan College, Bagnan, Howrah-711303, W.B., India

ABSTRACT

In this paper we have obtained some novel generating functions of -a modification of Gegenbauer polynomials, by utilizing L. Wesiner’s grouptheoretic method. By giving suitable interpretations to both the index (n) and the parameter (λ) of the polynomial under consideration, we obtain, in section 2, a set of infinitesimal operators known as raising and the lowering operators which generates a four dimensional Lie algebra. Finally, in Section 3, a novel generating function of the modified Gegenbauer polynomials which in turn yields a number of new and known results on generating functions.

KEYWORDS
Gegenbauer Polynomial, Generating Functions

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] K.P. Samanta , B. C. Chandra , C.S.Bera , "Some Generating Functions of Modified Gegenbauer Polynomials by Lie Algebraic Method," Mathematics and Statistics, Vol. 2, No. 4, pp. 172 - 178, 2014. DOI: 10.13189/ms.2014.020403.

(b). APA Format:
K.P. Samanta , B. C. Chandra , C.S.Bera (2014). Some Generating Functions of Modified Gegenbauer Polynomials by Lie Algebraic Method. Mathematics and Statistics, 2(4), 172 - 178. DOI: 10.13189/ms.2014.020403.