Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infinite series representations for Bessel functions of the first kind
  of integer order   We have discovered three non-power infinite series representations for Bessel
functions of the first kind of integer orders and real arguments. These series
contain only elementary functions and are remarkably simple. Each series was
derived as a Fourier series of a certain function that contains Bessel
function. The series contain parameter $b$ by setting which to specific values
one can change specific form of series. Truncated series retain qualitatively
behaviour of Bessel functions at large $x$: they have sine-like shape with
decreasing amplitude. Derived series allow to obtain new series expansions for
trigonometric functions.

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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn