Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Cosecant Numbers and the Hurwitz Zeta Function   This announcement paper summarises recent development concerning the
generalized cosecant numbers $c_{\rho,k}$, which represent the coefficients of
the power series expansion for the important fundamental function
$z^{\rho}/\sin^{\rho} z$. These coefficients are obtained for all, including
complex, values of $\rho$ via the partition method for a power series
expansion, which is more versatile than the standard Taylor series approach,
but yields the same results as the latter when both can be applied, though in a
different form. Surprisingly, the generalized cosecant numbers are polynomials
in $\rho$ of degree $k$, where $k$ is the power of $z$. General formulas for
the coefficients of the highest order terms in the generalized cosecant numbers
are presented. It is then shown how the generalized cosecant numbers are
related to the specific symmetric polynomials from summing over quadratic
powers of integers. Consequently, integral values of the Hurwitz zeta function
for even powers are expressed for the first time ever in terms of ratios of the
generalized cosecant numbers.

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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn