On the Hurwitz Zeta Function of Imaginary Second Argument

Abstract

In this work we exploit Jonquière's formula relating the Hurwitz zeta function to a linear combination of polylogarithmic functions in order to evaluate the real and imaginary part of ${\zeta }_H(s,ia)$ and its first derivative with respect to the first argument $s$. In particular, we obtain expressions for the real and imaginary party of ${\zeta }_H(s,ia)$ and its derivative for $s=m$ with $m\in \mathbb{Z}\backslash \{1\}$ involving simpler transcendental functions.

LaTeX, 15 pages

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• Analytic results for the effective action
• Schwinger Pair Production at Finite Temperature in QED
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Cited by in corpus (2)

• Remarks on the large-$N$ $\mathbb{C}{P}^{N-1}$ model
• Vacuum instability in Kaluza-Klein manifolds