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

Date: 2024..07..15
Event: 9th European Congress of Mathematics
Venue: Seville, Spain.

Abstract

One may consider the generalization of Jacobi polynomials and the Jacobi function 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 functions. In a similar fashion as associated Legendre functions, these break into two categories: functions that are analytically continued from the real line segment \((-1,1)\) and those continued from the real ray.

Using properties of Gauss hypergeometric functions, we derive multi-derivative and multi- integral representations for the Jacobi functions of the first and second kind.

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