Some properties of a class of generalized legendre’s associated functions

Quadratic Expansions of Generalized Legendre's Associated Functions

“…KUTPERS and B. METJLENBELD*. 1. In previous papers ( [1], [2]) we considered the differential equation: n dw ( m 2 n 2 2 l and defined two solutions P%-n (z) and Q™ >n {z) of (1) for all points of the z-plane in which a crosscut exists along the real axis from 1 to -oo.…”

“…1. In previous papers ( [1], [2]) we considered the differential equation: n dw ( m 2 n 2 2 l and defined two solutions P%-n (z) and Q™ >n {z) of (1) for all points of the z-plane in which a crosscut exists along the real axis from 1 to -oo. In [3] we gave tables of expansions for these functions in terms of hypergeometric functions F{a, b; c; £}, where £ is a linear function of z.…”

An extension of Neumann’s integralrelation for generalized Legendre functions

“…In Theorem 2 replace m by -m and n by -n, use (5) for the left-hand side and (13) for the right-hand side, split up the integral in the right-hand side (this is allowed because both integrals exist under given conditions) and in the integral involving P'(-x) change x into -x. This completes the proof.…”