Addition theorems for Legendre functions as corollaries of an addition theorem for Gegenbauer polynomials

Proofs are given for addition theorems for Legendre functions with arbitrary upper and lower indices, based solely on an addition theorem for Gegenbauer polynomials. New versions of these and other similar theorems are given, both in the form of sums and of integrals.Translated from Matematicheskie Zametki, Vol. 20, No. 3, pp. 321–330, September, 1976.