BILATERAL GENERATING FUNCTION FOR Pαn(x; h) AND Qαn(x; h)
1Lakshmi Narayan Mishra, 2Rakesh Kumar Singh and 3Shiv Kant Tiwari
1Department of Mathematics, School of Advanced Sciences,
Vellore Institute of Technology (VIT) University, Vellore 632014, Tamil Nadu, India
2Department of Mathematics, Jagdam College Chapra, Constitute unit of J. P. University, Chapra 841301, Bihar, India
3Department of Science and Humanities, Lukhdhirji Engineering College, Morbi-363642, Gujarat, India Email:firstname.lastname@example.org, email@example.com, firstname.lastname@example.org
(Received: September 10, 2020; In format: September 14, 2020; Revised in final form : November 02, 2021)
Our aimed has been made to find out forms of two interesting properties of the biorthogonal polynomials sets Pαn(x; h) AND Qαn(x; h) . In this paper, we have generalized the generating functions of biorthogonal polynomials suggested by the Laguerre polynomials published in Pacific Journal of Mathematics (1967) and some more results of transformation of certain bilinear generating functions published in Annali di Mathematica Pura ed Applicata (1970) with the help of some applicable results of the hand book of mathematical functions with formulas, graphs and mathematical tables (1964).
2020 Mathematical Sciences Classification: 33D15, 33D10, 33E05
Keywords and Phrases: Biorthogonal polynomial; Bilateral generating function.