Result: Generating Functions for polynomials Like Hermite polynomials containing Stirling numbers of the second kind

2010 Mathematics Subject Classification: 11B73, 42C05, 33C45 Abstract: The knowledge of generating function of a given set of special functions is crucial in obtaining various properties such as recurrence relation, differential equations satisfied by them. According to the Rainville [ 5] earlier such properties of special functions were obtained by hit and miss method. With a view to build up a systematic treatment of the properties of special functions the generating function techniques are quite useful.The Classical orthogonal polynomials contains Jacobi polynomials, Laguerre polynomials ,Hermite polynomials and Bessel polynomials .Though the usual generating function for extended Jacobi polynomials has been obtained by different methods by several authors including Fujiwara [ 1 ], Thakre [ 9 ] ,Patil and Thakre [ 4 ],Patil and Jagtap [ 3 ].Jagtap ,Tipayle and Andhare [2 ] obtained generating functions for the Hermite polynomials type I, II and III (which are defined by Sinha [ 7 ]) using orthogonality condition ,in this paper we have obtained the generating function for polynomials like Hermite polynomials containing Stirling numbers of the second kind .we have obtained the generating function using Srivastava’s theoremThis is one of the applications of Srivastava's theorem some particular cases are also discussed