Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Closed-form formulas and properties of coefficients in Maclaurin's
  series expansion of Wilf's function composited by inverse tangent, square
  root, and exponential functions   In the paper, with the aid of the Fa\`a di Bruno formula, be virtue of
several identities for the Bell polynomials of the second kind, with the help
of two combinatorial identities, by means of the (logarithmically) complete
monotonicity of generating functions of several integer sequences, and in the
light of Wronski's theorem, the authors establish Taylor's series expansions of
several functions involving the inverse (hyperbolic) tangent function, find out
Maclaurin's series expansion of a complex function composited by inverse
tangent, square root, and exponential functions and posed by Herbert S. Wilf,
and analyze some properties, including generating functions, limits,
positivity, monotonicity, and logarithmic convexity, of the coefficients in
Maclaurin's series expansion of Wilf's function. These coefficients in
Maclaurin's series expansion of Wilf's function are closed-form expressions in
terms of the Stirling numbers of the second kind. The authors also derive a
closed-form formula for a sequence of special values of Gauss' hypergeometric
function, discover a closed-form formula for a sequence of special values of
the Bell polynomials of the second kind, present several infinite series
representations of the circular constant Pi and other sequences, recover an
asymptotic rational approximation to the circular constant Pi, and connect
several integer sequences by determinants.

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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
3
The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat