Vol. 35, No. 1, 1970

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ISSN: 0030-8730
On a set of polynomials suggested by Laguerre polynomials

Tilak Raj Prabhakar

Vol. 35 (1970), No. 1, 213–219
Abstract

Generating functions, integrals and recurrence relations are obtained for the polynomials Znα(x;k) in xk which form one set of the biorthogonal pair with respect to the weight function exxα over the interval (0,), the other set being that of polynomials in x.

A singular integral equation with Znα(x;k) in the kernel is solved in terms of a generalized Mittag-Leffler’s function and a unified formula for fractional integration and differentiation of the polynomials is derived.

Mathematical Subject Classification
Primary: 33.40
Secondary: 44.00
Milestones
Received: 13 January 1970
Published: 1 October 1970
Authors
Tilak Raj Prabhakar