Integral representations for $\zeta(3)$ with the inverse sine function

Masato Kobayashi

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Integral representations for $\zeta(3)$ with the inverse sine function

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arxiv 2108.01247 v1 pith:J7JYTV2P submitted 2021-08-03 math.NT

Masato Kobayashi This is my paper · ORCID

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keywords integralfunctioninverserepresentationssinezetaconsequenceewell

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abstract

We show four new integral representations for $\zeta(3)$ as a reformulation of Ewell (1990) and Yue-Williams (1993) with the inverse sine function and Wallis integral. As a consequence, we also show a local integral representation for the trilogarithm function.

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