Multi-integral representations for Jacobi functions of the first and second kind

Published

October 5, 2023

Author(s)

Howard Cohl, Roberto S. Costas-Santos

Abstract

One may consider the generalization of Jacobi polynomials and the Jacobi func- tion of the second kind to a general function where the index is allowed to be a complex number instead of a non-negative integer. These functions are referred to as Jacobi func- tions. In a similar fashion as associated Legendre functions, these break into two categories, functions which are analytically continued from the real line segment (−1, 1) and those con- tinued from the real ray (1, ∞). Using properties of Gauss hypergeometric functions, we derive multi-derivative and multi-integral representations for the Jacobi functions of the first and second kind.

Citation

Arab Journal of Basic and Applied Sciences

Pub Type

Journals

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Keywords

Jacobi functions, Jacobi polynomials, Integral representations, Rodrigues-type relations, generalized hypergeometric functions

Citation

Cohl, H. and Costas-Santos, R. (2023), Multi-integral representations for Jacobi functions of the first and second kind, Arab Journal of Basic and Applied Sciences, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=956191 (Accessed October 14, 2025)