Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Determining the Indeterminate: On the Evaluation of Integrals that
  connect Riemann's, Hurwitz' and Dirichlet's Zeta, Eta and Beta functions   By applying the inverse Mellin transform to some new and simple closed form
identities, a number of relationships are established that connect Riemann's
and Hurwitz' zeta functions and their alternating equivalents. Interesting
special cases involving improper integrals containing $\zeta(\sigma+it)$ and a
minimum of other functions in the integrand are identified. Many of these
integrals do not appear in the literature and can be verified numerically. In
one limit, the use of analytic continuation generates a family of improper
integrals containing only the real and imaginary parts of $\zeta(\sigma+it)$
with and without simple trigonometric factors; the associated closed form
contains an (unclassified) entity that has many of the attributes of an
essential singularity, but probably is not. Consequently, this means that the
associated integrals are indeterminate (i.e. non-single valued), so a new
symbol is introduced to label the indeterminism. The bulk of this paper studies
this singularity from several angles in an attempt to resolve the associated
ambiguities. This is done by establishing a self-consistent way to remove the
singularity and thereby evaluate members of the family. These new closed-form
identities provide insight into the value of integrals of general interest.
Some implications are proposed.

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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph