Integral representations for local dilogarithm and trilogarithm functions

2021/08/28 by Masato Kobayashi, Kobayashi, Masato
Materials Science · Mathematics · #Advanced Mathematical Identities #Mathematical functions and polynomials #Nonlinear Optical Materials Research #math.NT #msc:11M06 #msc:11M41

paper · pdf · doi:10.48550/arxiv.2108.12543

21 pages. This is the second version

arxiv created 2021/09/27 · arxiv updated 2021/09/28

Abstract

We show new integral representations for dilogarithm and trilogarithm functions on the unit interval. As a consequence, we also prove (1) new integral representations for Apery, Catalan constants, and Legendre chi functions of order 2, 3, (2) a lower bound for the dilogarithm function on the unit interval, (3) new Euler sums.

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