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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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A note on the moment generating function for the reciprocal gamma distribution
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by Staffan Wrigge PDF
Math. Comp. 42 (1984), 617-621 Request permission


In this note we consider the function $\varphi (t) = \smallint _0^\infty {e^{ - tx}}/\Gamma (x) dx$ and use the Euler-Maclaurin expansion with the step-length $h = 1/4$ to obtain some useful (from a numerical point of view) formulae. Numerical values of $\varphi (t)$ correct to 11D are given for $t = 0.0(0.1)5.0$.
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Math. Comp. 42 (1984), 617-621
  • MSC: Primary 65D20; Secondary 60E10, 62E15, 65U05
  • DOI:
  • MathSciNet review: 736457