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Some sums of Legendre and Jacobi polynomials. (English) Zbl 0980.33006

Summary: 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.

MSC:

33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
33E30 Other functions coming from differential, difference and integral equations
35C05 Solutions to PDEs in closed form
34B27 Green’s functions for ordinary differential equations
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