  This article deals with three types of mutually inverse series relating
Ferrers and associated Legendre functions of arbitrary complex indexes and
orders established on the base of integral representations by using a number of
generating functions (some of them are novel) for polynomials expressed in
terms of hypergeometric or generalized hypergeometric polynomials. High-order
asymptotics of above-mentioned polynomials are indicated. In particular, a
uniform asymptotics for Gegenbauer polynomials of degree n and index a-n is
obtained for large n. In special cases, the inverse series turn into novel
mutually inverse finite sums relating Gegenbauer or associated Legendre
polynomials of different arguments as well as into novel connection formulas
for Gegenbauer and associated Legendre polynomials.
