Unification and Application of Certain Hypergeometric Polynomials of Three Variables

R.K. Singh¹ , B.K. Singh²

1. Department of Mathematics, J.P. University, Chapra, India.
2. Department of Mathematics, J.P. University, Chapra, India.

Correspondence should be addressed to: brijendrakumarsingh111956@gmail.com.

Section:Research Paper, Product Type: Journal-Paper
Vol.7 , Issue.2 , pp.122-131, Apr-2020

Online published on Apr 30, 2020

Copyright © R.K. Singh, B.K. Singh . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In the present paper, a generalized hypergeometric polynomial set Rn(x1,x2,x3) has been defined by means of a generating relation which contains Appell`s functions of three variables in the notation of Burchnall and Chaundy associated with Lauricella function. The polynomial set covers as many as forty orthogonal and non-orthogonal polynomials and have been obtained with special cases such as Hermite, Laguerre, Bateman etc. These polynomials are of at most important for mathematicians, scientists and engineers. The theory of special function has been developed enormously during the last two hundred years. The polynomials and their orthogonal properties are of great importance in mathematical analysis, including differential equation, integral equation, mathematical physics etc. Many orthogonal polynomials have their applications in quantum mechanics, chemical kinetics, electromagnetic theory etc.

Key-Words / Index Term :
Appell Function, Generalized Hypergeometric Polynomial, Integral Representation, Lauricella function, Orthogonal Polynomial, Generating Relation

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