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On Hurwitz zeta function and Lommel functions
International Journal of Number Theory ( IF 0.5 ) Pub Date : 2020-06-26 , DOI: 10.1142/s1793042120400047
Atul Dixit 1 , Rahul Kumar 1
Affiliation  

We obtain a new proof of Hurwitz’s formula for the Hurwitz zeta function ζ(s,a) beginning with Hermite’s formula. The aim is to reveal a nice connection between ζ(s,a) and a special case of the Lommel function Sμ,ν(z). This connection is used to rephrase a modular-type transformation involving infinite series of Hurwitz zeta function in terms of those involving Lommel functions.

中文翻译:

关于 Hurwitz zeta 函数和 Lommel 函数

我们获得了 Hurwitz 的 Hurwitz zeta 函数公式的新证明ζ(s,一种)从 Hermite 公式开始。目的是揭示两者之间的良好联系ζ(s,一种)和 Lommel 函数的一个特例小号μ,ν(z). 该连接用于将涉及无限系列 Hurwitz zeta 函数的模型变换重新表述为涉及 Lommel 函数的变换。
更新日期:2020-06-26
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