Geodesic
Addition theorems for Legendre functions as corollaries of an addition theorem for Gegenbauer polynomials
Matematičeskie zametki, Tome 20 (1976) no. 3, pp. 321-330.

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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. 
@article{MZM_1976_20_3_a2,
     author = {N. N. Beloozerov},
     title = {Addition theorems for {Legendre} functions as corollaries of an addition theorem for {Gegenbauer} polynomials},
     journal = {Matemati\v{c}eskie zametki},
     pages = {321--330},
     publisher = {mathdoc},
     volume = {20},
     number = {3},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_3_a2/}
}
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N. N. Beloozerov. Addition theorems for Legendre functions as corollaries of an addition theorem for Gegenbauer polynomials. Matematičeskie zametki, Tome 20 (1976) no. 3, pp. 321-330. http://geodesic.mathdoc.fr/item/MZM_1976_20_3_a2/