Linear relations for Lauricella F_D functions and symmetric polynomial

2020/09/16 by Krasoń, Piotr, Milewski, Jan
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2009.07467

Abstract

In this paper we develop an algorithm for obtaining some new linear relations among the Lauricella F_D functions. Relations we obtain, generalize those hinted in the work of B. C. Carlson. The coefficients of these relations are contained in the ring of polynomials in the variables x₁,…,x_N or in some exceptional cases in the field of rational functions \mathbb R(x₁,…,x_N,p). The method is based on expressing suitably chosen Euler type indefinite integrals associated with these functions recursively as linear combination of some other Euler type integrals and elementary functions and then integrating over the interval [0,1]. We describe the complete algorithm for obtaining these relations. We believe that such relations might be useful in computations.

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