Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Short Note on Integral Transformations and Conversion Formulas for
  Sequence Generating Functions   The purpose of this note is to provide an expository introduction to some
more curious integral formulas and transformations involving generating
functions. We seek to generalize these results and integral representations
which effectively provide a mechanism for converting between a sequence's
ordinary and exponential generating function (OGF and EGF, respectively) and
vice versa. The Laplace transform provides an integral formula for the
EGF-to-OGF transformation, where the reverse OGF-to-EGF operation requires more
careful integration techniques. We prove two variants of the OGF-to-EGF
transformation integrals from the Hankel loop contour for the reciprocal gamma
function and from Fourier series expansions of integral representations for the
Hadamard product of two generating functions, respectively. We also suggest
several generalizations of these integral formulas and provide new examples
along the way.

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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph