Vol. 90, No. 1, 1980

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ISSN: 0030-8730
A note on the Konhauser sets of biorthogonal polynomials suggested by the Laguerre polynomials

H. M. (Hari Mohan) Srivastava

Vol. 90 (1980), No. 1, 197–200
Abstract

Two new classes of bilateral generating functions are given for the Konhauser polynomials Y nα(x;k), which are biorthogonal to the Konhauser polynomials Znα(x;k) with respect to the weight function xαex over the interval (0,), α > 1 and k = 1,2,3, . The bilateral generating functions (1) and (2) below would reduce, when k = 1, to similar results for the generalized Laguerre polynomials Ln(α)(x). Furthermore, for k = 2, these formulas yield the corresponding properties of the Preiser polynomials.

It is also shown how the bilateral generating function (2) can be applied to derive a new generating function for the product

Ynα−kn(x;k)Z βn(y;l),

where α,β > 1, k,l = 1,2,3, , and n = 0,1,2, .

Mathematical Subject Classification
Primary: 33A65, 33A65
Milestones
Received: 2 November 1979
Published: 1 September 1980
Authors
H. M. (Hari Mohan) Srivastava