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Numerous novel integral and series representations for Ferrers functions ofthe first kind (associated Legendre functions on the cut) of arbitrary degreeand order, various integral, series and differential relations connectingFerrers functions of different orders and degrees as well as a uniformasymptotic expansion are derived in this article. Simple proofs of fourgenerating functions for Ferrers functions are given. Addition theorems forFerrers functions of the argument tanh(a+b) are proved by basing on generationfunctions for three families of hypergeometric polynomials. Relations forGegenbauer polynomials and Ferrers associated Legendre functions (associatedLegendre polynomials) are obtained as special cases.

Ferrers functions of arbitrary degree and order and related functions