Integral Evaluation of Odd Euler Sums, Multiple $t$-Value $t\left(3,2,\ldots,2\right)$ and Multiple Zeta Value $\zeta(3,2,\ldots,2)$

Jorge Layja; Masato Kobayashi; Sarth Chavan

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Integral Evaluation of Odd Euler Sums, Multiple $t$-Value $t\left(3,2,\ldots,2\right)$ and Multiple Zeta Value $\zeta(3,2,\ldots,2)$

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arxiv 2111.07097 v1 pith:QSHNXCCR submitted 2021-11-13 math.NT

Sarth Chavan , Masato Kobayashi , Jorge Layja This is my paper · ORCID

classification math.NT

keywords ldotsmultiplevaluezetaleftrighteulersums

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abstract

We construct an analytic approach to evaluate odd Euler sums, multiple zeta value $\zeta(3,2,\ldots,2)$ and multiple $t$-value $t\left(3,2,\ldots,2\right)$. Moreover, we also conjecture a closed expression for multiple $t$-value $t\left(2,\ldots,2,1\right)$.

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