CONVOLUTION INTEGRAL-EQUATIONS WITH GEGENBAUER FUNCTION KERNEL

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:50

Article; Proceedings Paper

VANBERKEL, CAM ; VANEIJNDHOVEN, SJL

关键词: GEGENBAUER FUNCTIONS;    GEGENBAUER TRANSFORMATIONS;    RODRIGUES FORMULA;    FRACTIONAL CALCULUS;    INTEGRAL EQUATIONS;   

DOI  :  10.1016/0377-0427(94)90328-X

来源: Elsevier

【 摘 要 】

In this paper we develop a concise and transparent approach for solving Mellin convolution equations where the convolutor is the product of an algebraic function and a Gegenbauer function. Our method is primarily based on (1) the use of fractional integral/differential operators; (2) a formula for Gegenbauer functions which is a fractional extension of the Rodrigues formula for Gegenbauer polynomials (see Theorem 3); (3) an intertwining relation concerning fractional integral/differential operators (see Theorem 1), which in the integer case reads (d/dx)2n+1 = (x-1d/dx)nx2n+1(x-1d/dx)n+1. Thus we cover most of the known results on this type of integral equations and obtain considerable extensions. As a special illustration we present the Gegenbauer transform pair associated to the Radon transformation.

【 授权许可】

Free