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Evaluation of one-dimensional polylogarithmic integral, with applications to infinite series

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arxiv 2007.03957 v4 pith:ARLWGUXD submitted 2020-07-08 math.NT math.CA

Kam Cheong Au This is my paper · ORCID
classification math.NTmath.CA
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We give systematic method to evaluate a large class of one-dimensional integral relating to multiple zeta values (MZV) and colored MZV. We also apply the technique of iterated integrals and regularization to elucidate the nature of some infinite series involving binomial coefficients. This technique can be applied to many Ap\'ery-type infinite sums.

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  1. Weighted Derivative Sums of a Gamma Quotient: Sun's Conjecture and Cyclotomic Specializations

    math.GM 2026-07 conditional novelty 6.0 of 10

    Weighted master identity for Γ(x)²/(2Γ(2x)) gives all-derivative-order sums in zeta and log-sine values and proves Sun's Conjecture 4.1.

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