Cohl, H.S. , COSTAS SANTOS, ROBERTO SANTIAGO, Durand, L. , Montoya, C. , Olafsson, G.
No
Conference Paper
Científica
01/01/2025
2-s2.0-105005281380
In this paper, we review and derive hyperbolic and trigonometric double summation addition theorems for Jacobi functions of the ?rst and second kind. In connection with these addition theorems, we perform a full analysis of the relation between (i) Jacobi functions with symmetric, antisymmetric, and half odd integer parameter values, and (ii) certain Gauss hypergeometric functions that satisfy a quadratic transformation, including associated Legendre, Gegenbauer and Ferrers functions of the ?rst and second kind. We also introduce Olver normalizations of the Jacobi functions, which are particularly useful in the derivation of expansion formulas when the parameters are integers. We apply the addition theorems for Jacobi functions of the second kind to separated eigenfunction expansions of fundamental solutions of Laplace–Beltrami operators on compact and noncompact rank-one symmetric spaces. © 2025 American Mathematical Society.
Addition theorems; Jacobi function of the ?rst kind; Jacobi function of the second kind; Jacobi polynomials; ultraspherical polynomials