Efficient Legendre polynomials transforms: from recurrence relations to Schoenberg's theorem

Abstract

We report results on various techniques which allow to compute the expansion into Legendre (or in general Gegenbauer) polynomials in an efficient way. We describe in some detail the algebraic/symbolic approach already presented in Ref.1 and expand on an alternative approach based on a theorem of Schoenberg.

10 pages, 8 figures