Vol. 42, No. 3, 1972

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A class of bilateral generating functions for certain classical polynomials

J. P. Singhal and H. M. (Hari Mohan) Srivastava

Vol. 42 (1972), No. 3, 755–762

In this paper the authors first prove a theorem on bilateral generating relations for a certain sequence of functions. It is then shown how the main result can be applied to derive a large variety of bilateral generating functions for the Bessel, Jacobi, Hermite, Laguerre and ultraspherical polynomials, as well as for their various generalizations. Some recent results given by W. A. Al-Salam [1], S. K. Chatterjea [2], M. K. Das [3], S. Saran [6] and the present authors [9] are thus observed to follow fairly easily as special cases of the theorem proved in this paper.

Mathematical Subject Classification
Primary: 33A65
Secondary: 33A45
Received: 21 June 1971
Published: 1 September 1972
J. P. Singhal
H. M. (Hari Mohan) Srivastava