منابع مشابه
Analytic continuation of multiple Hurwitz zeta functions
We use a variant of a method of Goncharov, Kontsevich, and Zhao [Go2, Z] to meromorphically continue the multiple Hurwitz zeta function ζd(s; θ) = ∑ 0<n1<···<nd (n1 + θ1) −s1 · · · (nd + θd)d , θk ∈ [0, 1), to C, to locate the hyperplanes containing its possible poles, and to compute the residues at the poles. We explain how to use the residues to locate trivial zeros of ζd(s; θ).
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This paper investigates a generalization the classical Hurwitz zeta function. It is shown that many of the properties exhibited by this special function extends to class of functions called hypergeometric Hurwitz zeta functions, including their analytic continuation to the complex plane and a pre-functional equation satisfied by them. As an application, a formula for moments of hypergeometric H...
متن کاملThe Magnetized Electron Gas in terms of Hurwitz Zeta Functions
We obtain explicit expressions for thermodynamic quantities of a relativistic degenerate free electron gas in a magnetic field in terms of Hurwitz Zeta functions. The formulation allows for systematic expansion in all regimes. Three energy scales appear naturally in the degenerate relativistic gas: the Fermi energy EF, the temperature T and an energy related to the magnetic field or Landau leve...
متن کاملGeometric Studies on Inequalities of Harmonic Functions in a Complex Field Based on ξ-Generalized Hurwitz-Lerch Zeta Function
Authors, define and establish a new subclass of harmonic regular schlicht functions (HSF) in the open unit disc through the use of the extended generalized Noor-type integral operator associated with the ξ-generalized Hurwitz-Lerch Zeta function (GHLZF). Furthermore, some geometric properties of this subclass are also studied.
متن کاملOn Some Integrals Involving the Hurwitz Zeta
We establish a series of integral formulae involving the Hurwitz zeta function. Applications are given to integrals of Bernoulli polynomials, log Γ(q) and log sin(q).
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 2017
ISSN: 0386-2194
DOI: 10.3792/pjaa.93.31