New formulas for the linearization coefficients of some nonsymmetric Jacobi polynomials

The main aim of this paper is to develop four innovative linearization formulas for some nonsymmetric Jacobi polynomials. This means that we find the coefficients of the products of Jacobi polynomials of certain parameters. In general, these coefficients are expressed in terms of certain hypergeomet...

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Bibliographic Details
Published in:Advances in difference equations Vol. 2015; no. 1; pp. 1 - 13
Main Author: Abd-Elhameed, Waleed M
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 04.06.2015
Springer Nature B.V
Subjects:
Algebra
Algorithms
Analysis
Difference and Functional Equations
Formulas (mathematics)
Functional Analysis
Hypergeometric functions
Linearization
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Polynomials
Stopping
Transformations (mathematics)
Jacobi polynomials
42C10
33C25
hypergeometric functions
recurrence relations
33D45
symbolic computation
33A50
linearization coefficients
ISSN:1687-1847, 1687-1839, 1687-1847
Online Access:Get full text
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Summary:The main aim of this paper is to develop four innovative linearization formulas for some nonsymmetric Jacobi polynomials. This means that we find the coefficients of the products of Jacobi polynomials of certain parameters. In general, these coefficients are expressed in terms of certain hypergeometric functions of the unit argument. We employ some symbolic algebraic computations such as the algorithms of Zeilberger, Petkovsek and van Hoeij for reducing such coefficients. Moreover, and based on a certain Whipple transformation, two new closed formulas for summing certain terminating hypergeometric functions of the unit argument are deduced. New formulas for some definite integrals are given with the aid of the derived linearization formulas.
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ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-015-0509-4