A multilinear generating function for the Konhauser sets of biorthogonal polynomials suggested by the Laguerre polynomials

The polynomial sets {Y _n^α(x;k)} and {Z_n^α(x;k)}, discussed by Joseph D. E. Konhauser, are biorthogonal over the interval (0,∞) with respect to the weight function x^αe^−x, where α > −1 and k is a positive integer. The object of the present note is to develop a fairly elementary method of proving a general multilinear generating function which, upon suitable specializations, yields a number of interesting results including, for example, a multivariable hypergeometric generating function for the multip sum:

∑∞ α
(m + n1 + ⋅⋅⋅+ nr)!Y m+n1+⋅⋅⋅+nr(x;k)
n1,...,nr=0
∏r Z-βnii(yi;si)unii
⋅ { (1+ βi)sini }, (*)
i=1

involving the Konhauser biorthogonal polynomials; here, by definition,

α > − 1; βi > − 1; k,si = 1,2,3,...; ∀i ∈ {1,...,r}.

Mathematical Subject Classification

Primary: 33A30, 33A30

Milestones

Received: 22 December 1982

Published: 1 March 1985

Authors

H. M. (Hari Mohan) Srivastava

Vol. 117, No. 1, 1985

H. M. (Hari Mohan) Srivastava

Abstract

Mathematical Subject Classification

Milestones

Authors