Novel Formulae of Certain Generalized Jacobi Polynomials

Waleed Mohamed Abd-Elhameed ()
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Waleed Mohamed Abd-Elhameed: Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt

Mathematics, 2022, vol. 10, issue 22, 1-25

Abstract: The main goal of this article is to investigate theoretically a kind of orthogonal polynomials, namely, generalized Jacobi polynomials ( G J P s ). These polynomials can be expressed as certain combinations of Legendre polynomials. Some basic formulas of these polynomials such as the power form representation and inversion formula of these polynomials are first introduced, and after that, some interesting formulas concerned with these polynomials are established. The formula of the derivatives of the moments of these polynomials is developed. As special cases of this formula, the moment and high-order derivative formulas of the G J P s are deduced. New expressions for the high-order derivatives of the G J P s , but in terms of different symmetric and non-symmetric polynomials, are also established. These expressions lead to some interesting connection formulas between the G J P s and some various polynomials.

Keywords: Legendre polynomials; generalized Jacobi polynomials; Chebyshev polynomials; linearization and connection coefficients; generalized hypergeometric functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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