Abstract
In this paper we present integral representations for products of Lamé functions based on the theory of fundamental solutions. The kernels of these representations involve Legendre functions of the second kind. In particular, we generalize and improve integral representations for external ellipsoidal harmonics mentioned by Erdélyi, Magnus, Oberhettinger and Tricomi [Higher Transcendental Functions III, McGraw Hill, New York, 1955] and for Lamé functions of the second kind in terms of Lamé polynomials studied by Shall [SIAM J. Math. Anal., 11 (1980), pp. 702–723].
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