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Legendre polynomials; Jacobi polynomials; polylogarithms
We prove identities involving sums of Legendre and Jacobi polynomials. The identities are related to Green’s functions for powers of the invariant Laplacian and to the Minakshisundaram-Pleijel zeta function.
[1] M. Engliš, J. Peetre: Green’s functions for powers of the invariant Laplacian. Canad J. Math. 50 (1998), 40–73. DOI 10.4153/CJM-1998-004-8 | MR 1618718
[2] L. Lewin: Structural Properties of Polylogarithms. Math. Surveys Monographs 37, American Mathematical Society, Providence, RI, 1991. MR 1148371 | Zbl 0745.33009
[3] Y. L. Luke: The Special Functions and Their Approximation. Volume I. Academic Press, New York, London, 1969. MR 0241700
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