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Some novel generating functions of extended Jacobi polynomials by group theoretic method. (English) Zbl 0902.33008

In this paper the authors make use of Weisner’s group method to obtain certain generating relations for extended Jacobi polynomials which were introduced by K. R. Patil and N. K. Thakare [Math. Stud. 45, No. 1, 41-51 (1977; Zbl 0591.47036)].

MSC:

33C80 Connections of hypergeometric functions with groups and algebras, and related topics
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)

Citations:

Zbl 0591.47036
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References:

[1] Patil, K.R. and Thakare, N.K.: Operational formulae and generating function in the united form for the classical orthogonal polynomials. Mathematics Student 46 (1977), no. 1, 41-51. · Zbl 0591.47036
[2] Shrivastava, P.N. and Dhillon, S.S.: Lie operator and classical orthogonal polynomials. Pure Math. Manuscript 7 (1988), 129-136. · Zbl 0726.33009
[3] Chongdar, A.K. and Pan, S.K.: Quelques fonctions génératrices de certains polynômes orthogonaux du point de vue du groupe Lie.
[4] Weisner, L.: Group theoretic origin of certain generating functions. Pacific J. Math. 5 (1955), 1033-1039. · Zbl 0067.29401
[5] McBride, E.B.: Obtaining Generating Functions. Springer Verlag, Berlin, 1972. · Zbl 0215.43403
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