Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The asymptotic expansion of a generalisation of the Euler-Jacobi series   We consider the asymptotic expansion of the sum \[S_p(a;w)=\sum_{n=1}^\infty
n^{-w}\e^{-an^p}\] as $a\rightarrow 0$ in $|\arg\,a|<\pi/2$ for arbitrary
finite $p>$ and $w>0$. Our attention is concentrated mainly on the case when
$p$ and $w$ are both even integers, where the expansion consists of a {\it
finite} algebraic expansion together with a sequence of increasingly
subdominant exponential expansions. This exponentially small component produces
a transformation for $S_p(a;w)$ analogous to the well-known Poisson-Jacobi
transformation for the sum with $p=2$ and $w=0$. Numerical results are given to
illustrate the accuracy of the expansion obtained.

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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: ao-sci