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An integral relation for tensor polynomials
Authors:P A Vshivtseva  V I Denisov  I P Denisova
Institution:(1) Duke University, Durham, NC, USA;(2) Radboud University Nijmegen, Nijmegen, The Netherlands;
Abstract: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.
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