Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic Approximations to Truncation Errors of Series Representations
  for Special Functions   Asymptotic approximations ($n \to \infty$) to the truncation errors $r_n = -
\sum_{\nu=0}^{\infty} a_{\nu}$ of infinite series $\sum_{\nu=0}^{\infty}
a_{\nu}$ for special functions are constructed by solving a system of linear
equations. The linear equations follow from an approximative solution of the
inhomogeneous difference equation $\Delta r_n = a_{n+1}$. In the case of the
remainder of the Dirichlet series for the Riemann zeta function, the linear
equations can be solved in closed form, reproducing the corresponding
Euler-Maclaurin formula. In the case of the other series considered -- the
Gaussian hypergeometric series ${}_2 F_1 (a, b; c; z)$ and the divergent
asymptotic inverse power series for the exponential integral $E_1 (z)$ -- the
corresponding linear equations are solved symbolically with the help of Maple.
The practical usefulness of the new formalism is demonstrated by some numerical
examples.

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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int