On values of the higher derivatives of the Barnes zeta function at non-positive integers
نویسندگان
چکیده
Let $x$ be a complex number which has positive real part, and $w_1,\ldots,w_N$ rational numbers. We show that $w^s \zeta_N (s, x \ |\ w_1,\ldots, w_N)$ can expressed as finite linear combination of the Hurwitz zeta functions over $\mathbf Q(x)$, where $\zeta_N (s,x is Barnes function $w$ explicitly determined by $w_1,\ldots, w_N$. Furthermore, we give generalizations Kummer's formula on gamma Koyama-Kurokawa's formulae multiple functions, an explicit for values at non-positive integers higher order derivatives in case number, involving generalized Stieltjes constants Riemann function. Our also makes it possible to calculate approximation $w_1, \ldots, w_N$ are
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ژورنال
عنوان ژورنال: Kodai Mathematical Journal
سال: 2022
ISSN: ['0386-5991', '1881-5472']
DOI: https://doi.org/10.2996/kmj/kmj45105