Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Series Representation for Riemann's Zeta Function and some Interesting
  Identities that Follow   Using Cauchy's Integral Theorem as a basis, what may be a new series
representation for Dirichlet's function $\eta(s)$, and hence Riemann's function
$\zeta(s)$, is obtained in terms of the Exponential Integral function
$E_{s}(i\kappa)$ of complex argument. From this basis, infinite sums are
evaluated, unusual integrals are reduced to known functions and interesting
identities are unearthed. The incomplete functions $\zeta^{\pm}(s)$ and
$\eta^{\pm}(s)$ are defined and shown to be intimately related to some of these
interesting integrals. An identity relating Euler, Bernouli and Harmonic
numbers is developed. It is demonstrated that a known simple integral with
complex endpoints can be utilized to evaluate a large number of different
integrals, by choosing varying paths between the endpoints.

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The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
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The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat