Jacobi polynomials and some related functions

Abstract

The classical Jacobi orthogonal polynomials (especially their special case—the Legendre polynomials) appear as the solutions of some problems of mathematical physics. In the contribution we deal with some relations connecting generalized Legendre polynomials of a certain type and the classical Jacobi polynomials orthogonal with respect to two different special weight functions. We also point out relations between the classical Legendre polynomials, the associated Legendre functions of the first kind, the Legendre functions of the first kind and the generalized g-Legendre functions obtained by Mirevski et al. using fractional calculus.