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Vol.2 , No. 6, Publication Date: Jan. 12, 2016, Page: 79-90
 and confluent hypergeometric function (CHF). The main object of this paper is to express explicitly the derivatives of generalized Jacobi polynomials in terms of Jacobi polynomials themselves, by using generalized hypergeometric functions of any degree that have been differentiated an arbitrary numbers of times. The results for the special cases of generalized Ultraspherical polynomials and Chebyshev polynomials of the first, second, third and fourth kinds and Legendre polynomials are also given.&picture=http://www.aascit.org/aascit/decorators/img/journal/921.jpg)
| [1] | S. I. El-Soubhy, Department of Mathematics, College of Science, Taibah University, Almadinah Almunawwarah, Saudi Arabia. |
Recently, some generalizations of the generalized gamma, beta, Gauss hypergeometric and confluent hypergeometric functions have been introduced in the literature. Most of the special functions, such as Jacobi polynomials, can be expressed in terms of Gauss hypergeometric function (GHF) and confluent hypergeometric function (CHF). The main object of this paper is to express explicitly the derivatives of generalized Jacobi polynomials in terms of Jacobi polynomials themselves, by using generalized hypergeometric functions of any degree that have been differentiated an arbitrary numbers of times. The results for the special cases of generalized Ultraspherical polynomials and Chebyshev polynomials of the first, second, third and fourth kinds and Legendre polynomials are also given.
Keywords
Spectral and Pseudo Spectral Methods, Orthogonal Polynomials, Jacobi Polynomials, Ultrspherical Polynomials, Gamma Function, Beta Function, Hypergeometric Function, Confluent Hypergeometric Function
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