Geodesic
An~integral relation for tensor polynomials
Teoretičeskaâ i matematičeskaâ fizika, Tome 166 (2011) no. 2, pp. 216-224

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We prove two lemmas and one theorem that allow integrating the product of an arbitrary number of unit vectors and the Legendre polynomials over a sphere of arbitrary radius. Such integral tensor products appear in solving inhomogeneous Helmholtz equations whose right-hand side is proportional to the product of a nonfixed number of unit vectors.
Keywords: tensor relation, Gegenbauer theorem, pseudo-Riemannian geometry.
Mots-clés : tensor Legendre polynomial 
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     author = {P. A. Vshivtseva and V. I. Denisov and I. P. Denisova},
     title = {An~integral relation for tensor polynomials},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {166},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_166_2_a1/}
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P. A. Vshivtseva; V. I. Denisov; I. P. Denisova. An~integral relation for tensor polynomials. Teoretičeskaâ i matematičeskaâ fizika, Tome 166 (2011) no. 2, pp. 216-224. http://geodesic.mathdoc.fr/item/TMF_2011_166_2_a1/