  Numerous novel integral and series representations for Ferrers functions of
the first kind (associated Legendre functions on the cut) of arbitrary degree
and order, various integral, series and differential relations connecting
Ferrers functions of different orders and degrees as well as a uniform
asymptotic expansion are derived in this article. Simple proofs of four
generating functions for Ferrers functions are given. Addition theorems for
Ferrers functions of the argument tanh(a+b) are proved by basing on generation
functions for three families of hypergeometric polynomials. Relations for
Gegenbauer polynomials and Ferrers associated Legendre functions (associated
Legendre polynomials) are obtained as special cases.
