(R1454) On Reducing the Linearization Coefficients of Some Classes of Jacobi Polynomials

Authors

Waleed Abd-Elhameed, Cairo University
Afnan Ali, University of Jeddah

Abstract

This article is concerned with establishing some new linearization formulas of the modified Jacobi polynomials of certain parameters. We prove that the linearization coefficients involve hypergeometric functions of the type ₄F₃(1). Moreover, we show that the linearization coefficients can be reduced in several cases by either utilizing certain standard formulas, and in particular Pfaff-Saalschütz identity and Watson’s theorem, or via employing the symbolic algebraic algorithms of Zeilberger, Petkovsek, and van Hoeij. New formulas for some definite integrals are obtained with the aid of the developed linearization formulas.

Recommended Citation

Abd-Elhameed, Waleed and Ali, Afnan (2021). (R1454) On Reducing the Linearization Coefficients of Some Classes of Jacobi Polynomials, Applications and Applied Mathematics: An International Journal (AAM), Vol. 16, Iss. 2, Article 22.
Available at: https://digitalcommons.pvamu.edu/aam/vol16/iss2/22