A Sextuple Integral Containing the Product of Associated Legendre polynomials P_v^u(x) P_ν^μ(y): Derivation and Evaluation

2022/01/06 by Robert G. Reynolds, Reynolds, Robert, A D Stauffer +1
Mathematics · #30E20 #33-01 #33-03 #33-04 #33-33B #Advanced Mathematical Identities #FOS: Mathematics #General Mathematics (math.GM) #Mathematical Inequalities and Applications #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2201.02617

openalex publication_date 2022/01/06 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

In this present paper we derive a six dimensional integral containing the product of the Associated Legendre Polynomials P_v^u(x) P_ν ^μ (y) where the indices are different and general. Included in the kernel of this integral is the generalized logarithmic function and coefficient logarithmic functions. The derivation of this integral is written in terms of the Hurwitz-Lerch zeta function and constant coefficients raised to a power. Special cases of this integral are derived in terms of fundamental constants and other special functions. All the results in this work are new.

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