On the differential-difference properties of the extended Jacobi polynomials

Author:

Lewanowicz S.

Abstract

We discuss differential-difference properties of the extended Jacobi polynomials \[ P n ( x ) = p + 2 F q ( n , n + λ , a p ; b q ; x ) ( n = 0 , 1 , ) . {P_n}(x){ = _{p + 2}}{F_q}( - n,n + \lambda ,{a_p};{b_q};x)\quad (n = 0,1, \ldots ). \] The point of departure is a corrected and reformulated version of a differential-difference equation satisfied by the polynomials P n ( x ) {P_n}(x) , which was derived by Wimp (Math. Comp., v. 29, 1975, pp. 577-581).

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Reference7 articles.

1. Contiguous hypergeometric functions of the type ₃𝐹₂(1);Bailey, W. N.;Proc. Glasgow Math. Assoc.,1954

2. Recurrence relations for hypergeometric functions of unit argument;Lewanowicz, Stanisław;Math. Comp.,1985

3. Y. L. Luke, The Special Functions and Their Approximations, Academic Press, New York, 1969.

4. Recursion formulae for hypergeometric functions;Wimp, Jet;Math. Comp.,1968

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Differential-difference properties of hypergeometric series;Proceedings of the American Mathematical Society;2023-03-21

2. A Differential-Difference Equation;SIAM Journal on Mathematical Analysis;1987-05

3. RECURRENCE RELATIONS FOR HYPERGEOMETRIC-FUNCTIONS OF UNIT ARGUMENT;MATH COMPUT;1985

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