Zeta2(s1,s2),Zeta3(s1,s2,s3):Integral Expressions and Approximates

V. V. Rane

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arXiv · 1207.0763

Zeta2(s1,s2),Zeta3(s1,s2,s3):Integral Expressions and Approximates

V. V. Rane

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Abstract

For the multiple zeta function zeta2(s1,s2) of two variables,we obtain its integral representation(involving product of Hurwitz zeta functions) over the interval [1,infinity),with respect to second variable of Hurwitz zeta function and also obtain a good approximate to it as a function of s1 and s2,for s1>=1 and s2>1.In particular this approximate is explicitly computable,when s1,s2 differ by an even integer and is good,when s2 is large.We treat zeta3(s1,s2,s3) likewise.

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BibTeX RIS

V. V. Rane. 2012-07-03. Zeta2(s1,s2),Zeta3(s1,s2,s3):Integral Expressions and Approximates. https://arxiv.org/abs/1207.0763

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