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Integral Evaluation of Odd Euler Sums, Multiple t-Value tleft(3,2,ldots,2right) 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

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

classification math.NT
keywords ldotsmultiplevaluezetaleftrighteulersums
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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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