Abstract

This paper contains mainly three theorems involving Kamp$\acute{e}$ de F$\acute{e}$riet's function $F^{(2)}$ and expressed in terms of single and double Laplace and Beta integrals. The theorems, in turn, yield, as special cases, a number of linear, bilinear and bilateral generating functions of generalized polynomials of Rice, Jacobi polynomials, Ultraspherical, Generalized Laguerre, Bedient polynomials and other polynomials hypergeometric in nature. One variable special cases of generalized polynomials are useful in several applied problems.

Keywords and Phrases

Linear, Bilinear and Bilateral Generating Functions, Eulerian integrals of first and second kind; Hankel's contour integral, Kamp$\acute{e}$ de F$\acute{e}$riet's double hypergeometric function $F^{(2)}{[x,y]}$, Srivastava's triple hypergeometric function $F^{(3)}{[x,y,z]}$ and Orthogonal polynomials.

A.M.S. subject classification

33C05, 33C20, 33C45, 33C65, 33C70.

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