Rocky Mountain Journal of Mathematics

New linearization formulae for the products of Chebyshev polynomials of third and fourth kinds

E.H. Doha and W.M. Abd-Elhameed

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Abstract

This paper deals with the problem of finding two new closed formulae for linearization coefficients of two special nonsymmetric cases for Jacobi polynomials $P^{(\alpha ,\beta )}_n(x)$ corresponding to the parameters' values $\beta =-\alpha =\pm 1/2$. From these two formulae, the linearization coefficients of the products of Chebyshev polynomials of the third and fourth kinds are established. Based on using algorithmic methods, such as the algorithms by Zeilberger, Petkovsek and Van-Hoeij, and two certain Whipple's transformations, six new closed formulae for summing certain terminating hyper\-geometric functions of unit argument are given.

Article information

Source
Rocky Mountain J. Math., Volume 46, Number 2 (2016), 443-460.

Dates
First available in Project Euclid: 26 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1469537472

Digital Object Identifier
doi:10.1216/RMJ-2016-46-2-443

Mathematical Reviews number (MathSciNet)
MR3529078

Zentralblatt MATH identifier
1360.33013

Subjects
Primary: 33A50 33C25 33D45: Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

Keywords
Chebyshev polynomials of third and fourth kinds linearization coefficients recurrence relation algorithms by Zeilberger Petkovsek and Van-Hoeij

Citation

Doha, E.H.; Abd-Elhameed, W.M. New linearization formulae for the products of Chebyshev polynomials of third and fourth kinds. Rocky Mountain J. Math. 46 (2016), no. 2, 443--460. doi:10.1216/RMJ-2016-46-2-443. https://projecteuclid.org/euclid.rmjm/1469537472


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