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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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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