The present paper mainly concerns with three theorems involving generating functions expressed in terms of single and double Laplace and Beta integrals. These theorems have been applied to obtain bilinear and bilateral generating functions involving polynomials of Mittag- Lefler, Madhekar- Thakare, Gottlieb, Jacobi, Konhauser, Laguerre and other polynomials hypergeometric in nature. One variable special cases of the hypergeometric polynomials are important in several applied problems.
Keywords and Phrases
Bilinear and bilateral generating functions; Eulerian integrals of first and second kind; Hankel’s contour integral; Kamp´e de F´eriet’s double hypergeometric function; Srivastava’s triple hypergeometric function F (3) ; Orthogonal polynomials.
A.M.S. subject classiﬁcation
Primary 33A30; Secondary 33A65.