Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two General Series Identities Involving Modified Bessel Functions and a
  Class of Arithmetical Functions   We consider two sequences $a(n)$ and $b(n)$, $1\leq n<\infty$, generated by
Dirichlet series
  $$\sum_{n=1}^{\infty}\frac{a(n)}{\lambda_n^{s}}\qquad\text{and}\qquad
  \sum_{n=1}^{\infty}\frac{b(n)}{\mu_n^{s}},$$ satisfying a familiar functional
equation involving the gamma function $\Gamma(s)$. Two general identities are
established. The first involves the modified Bessel function $K_{\mu}(z)$, and
can be thought of as a 'modular' or 'theta' relation wherein modified Bessel
functions, instead of exponential functions, appear. Appearing in the second
identity are $K_{\mu}(z)$, the Bessel functions of imaginary argument
$I_{\mu}(z)$, and ordinary hypergeometric functions ${_2F_1}(a,b;c;z)$.
Although certain special cases appear in the literature, the general identities
are new. The arithmetical functions appearing in the identities include
Ramanujan's arithmetical function $\tau(n)$; the number of representations of
$n$ as a sum of $k$ squares $r_k(n)$; and primitive Dirichlet characters
$\chi(n)$.

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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn