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This article deals with three types of mutually inverse series relatingFerrers and associated Legendre functions of arbitrary complex indexes andorders established on the base of integral representations by using a number ofgenerating functions (some of them are novel) for polynomials expressed interms of hypergeometric or generalized hypergeometric polynomials. High-orderasymptotics of above-mentioned polynomials are indicated. In particular, auniform asymptotics for Gegenbauer polynomials of degree n and index a-n isobtained for large n. In special cases, the inverse series turn into novelmutually inverse finite sums relating Gegenbauer or associated Legendrepolynomials of different arguments as well as into novel connection formulasfor Gegenbauer and associated Legendre polynomials.

Mutually inverse series relating Ferrers and associated Legendre functions and generating functions pertaining to them