On a set of polynomials suggested by Laguerre polynomials

Tilak Raj Prabhakar

Vol. 35 (1970), No. 1, 213–219

DOI: 10.2140/pjm.1970.35.213

Abstract

Generating functions, integrals and recurrence relations are obtained for the polynomials Z_n^α(x;k) in x^k which form one set of the biorthogonal pair with respect to the weight function e^−xx^α over the interval (0,∞), the other set being that of polynomials in x.

A singular integral equation with Z_n^α(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