Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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AN ASYMPTOTIC EXPANSION FOR THE FIRST DERIVATIVE OF THE HURWITZ-TYPE EULER ZETA FUNCTION

  • MIN-SOO KIM (Department of Mathematics Education, Kyungnam University)
  • Received : 2023.08.30
  • Accepted : 2023.11.06
  • Published : 2023.11.30
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Abstract

The Hurwitz-type Euler zeta function ζE(z, q) is defined by the series ${\zeta}_E(z,\,q)\,=\,\sum\limits_{n=0}^{\infty}{\frac{(-1)^n}{(n\,+\,q)^z}},$ for Re(z) > 0 and q ≠ 0, -1, -2, . . . , and it can be analytic continued to the whole complex plane. An asymptotic expansion for ζ'E(-m, q) has been proved based on the calculation of Hermite's integral representation for ζE(z, q).

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Acknowledgement

This work was supported by the Kyungnam University Foundation Grant, 2022.

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