Multiple Stieltjes constants and Laurent type expansion of the multiple\n zeta functions at integer points

2019/02/12 by Biswajyoti Saha, Saha, Biswajyoti · 2 citations
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1902.04389

Abstract

In this article, we study the local behaviour of the multiple zeta functions\nat integer points and write down a Laurent type expansion of the multiple zeta\nfunctions around these points. Such an expansion involves a convergent power\nseries whose coefficients are obtained by a regularisation process, similar to\nthe one used in defining the classical Stieltjes constants for the Riemann zeta\nfunction. We therefore call these coefficients it multiple Stieltjes\nconstants. The remaining part of the above mentioned Laurent type expansion is\nthen expressed in terms of the multiple Stieltjes constants arising in smaller\ndepths.\n

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• Multiple polylogarithms, a regularisation process and an admissible open domain of convergence
• Values at non-positive integers of partially twisted multiple zeta-functions II

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