On the Poincaré expansion of the Hurwitz zeta function

被引：0

作者：

Bujar Fejzullahu

机构：

[1] University of Prishtina,Department of Mathematics

来源：

Lithuanian Mathematical Journal | 2021年 / 61卷

关键词：

Hurwitz zeta function; Poincaré expansion; exponential improved expansion; incomplete gamma function; Lommel functions; 11M35; 41A60; 30E15; 33C47;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In this paper, we extend the result of Paris [R.B. Paris, The Stokes phenomenon associated with the Hurwitz zeta function ζ(s, a), Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 461(2053):297–304, 2005] on the exponentially improved expansion of the Hurwitz zeta function ζ(s, z), the expansion of which can be reduced to the large-z Poincaré asymptotics of ζ(s, z). Furthermore, we deduce some new series and integral representations of the Hurwitz zeta function ζ(s, z).

引用

页码：460 / 470

页数：10

共 10 条

[1]

Dixit A(2021)On Hurwitz zeta function and Lommel functions Int. J. Number Theory 7 393-404

[2]

Kumar R(2016)Neumann series and Lommel functions of two variables Integral Transforms Spec. Funct. 27 443-453

[3]

Fejzullahu BX(2019)Partial fraction expansion of the hypergeometric functions Integral Transforms Spec. Funct. 30 240-253

[4]

Fejzullahu BX(2015)Rigorous high-precision computation of the Hurwitz zeta function and its derivatives Numer. Algorithms 69 253-270

[5]

Johansson F(2004)Some integral and asymptotic formulas associated with the Hurwitz zeta function Appl. Math. Comput. 154 641-664

[6]

Kanemitsu S(1997)Spaces of holomorphic functions equivalent to the even Maass cusp forms Invent. Math. 127 271-306

[7]

Kumagai H(undefined)undefined undefined undefined undefined-undefined

[8]

Srivastava HM(undefined)undefined undefined undefined undefined-undefined

[9]

Yoshimoto M(undefined)undefined undefined undefined undefined-undefined

[10]

Lewis JB(undefined)undefined undefined undefined undefined-undefined

← 1 →