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The Hurwitz-type Euler zeta function is defined as a deformation of the Hurwitz zeta function: \begin{equation*} \zeta_E(s,x)=\sum_{n=0}^\infty\frac{(-1)^n}{(n+x)^s}. \end{equation*} In this paper, by using the method of Fourier expansions, we shall evaluate several integrals with integrands involving Hurwitz-type Euler zeta functions $\zeta_E(s,x)$. Furthermore, the relations between the values of a class of the Hurwitz-type (or Lerch-type) Euler zeta functions at rational arguments have also been given.
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참고문헌 (40)
참고문헌 신청
M. Abramowitz / 1992 / Handbook of mathematical functions with formulas, graphs, and mathematical tables / Dover Publications, Inc.
V. Adamchik / 0000 / 32 representations for Catalan constant
T. M. Apostol / 1951 / On the Lerch zeta function / Pacific J. Math. 1:161~167
T. M. Apostol / 1954 / Some series involving the Riemann zeta function / Proc. Amer. Math. Soc. 5:239~243
T. M. Apostol / 1976 / Introduction to analytic number theory / Springer-Verlag
V. Adamchik / 0000 / 32 representations for Catalan constant
T. M. Apostol / 1951 / On the Lerch zeta function / Pacific J. Math. 1:161~167
T. M. Apostol / 1954 / Some series involving the Riemann zeta function / Proc. Amer. Math. Soc. 5:239~243
T. M. Apostol / 1976 / Introduction to analytic number theory / Springer-Verlag
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