Simultaneous Triple Series Equations Involving Konhauser Biorthogonal Polynomials

Abstract

Biorthogonal polynomials are of great interest for Physicists.Spencer and Fano (9) used the biorthogonal polynomials (for the case k = 2) in carrying out calculations involving penetration of gamma rays through matter.In the present paper an exact solution of simultaneous triple series equations involving Konhauser-biorthogonal polynomials of first kind of different indices is obtained by multiplying factor technique due to Noble. (4) This technique has been modified by Thakare (10, 11) to solve dual series equations involving orthogonal polynomials which led to disprove a possible conjecture of Askey (1) that a dual series equation involving Jacobi polynomials of different indices can not be solved. In this paper the solution of simultaneous triple series equations involving generalized Laguerre polynomials also have been discussed as a charmfull particular case. n=0 −1 q p q=0 p q q+α+1 k n