On Polar Legendre Polynomials

Details On Polar Legendre Polynomials On Polar Legendre Polynomials

2007-09-28

arxiv.org/abs/0709.4537v1

Mathematics

Classical Analysis and ODEs

Scientific paper

We introduce a new class of polynomials $\{P_{n}\}$, that we call polar Legendre polynomials, they appear as solutions of an inverse Gauss problem of equilibrium position of a field of forces with $n+1$ unit masses. We study algebraic, differential and asymptotic properties of this class of polynomials, that are simultaneously orthogonal with respect to a differential operator and a discrete-continuous Sobolev type inner product.

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