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A note on the moment generating function for the reciprocal gamma distribution

Author: Staffan Wrigge
Journal: Math. Comp. 42 (1984), 617-621
MSC: Primary 65D20; Secondary 60E10, 62E15, 65U05
MathSciNet review: 736457
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Abstract: 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$.

References [Enhancements On Off] (What's this?)

  • [1] M. G. Kendall & A. Stuart, The Advanced Theory of Statistics, Vol. I, Charles Griffin & Company Limited, 1958.
  • [2] D. F. Kerridge & G. W. Cook, "Yet another series for the normal integral," Biometrika, v. 63, 1976, pp. 401-403.
  • [3] A. Fransén & S. Wrigge, "Calculation of the moments and the moment generating function for the reciprocal gamma distribution," Math. Comp., v. 42, 1984, pp. 601-616. MR 736456 (86f:65042a)

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Keywords: Reciprocal gamma distribution, generating function, Euler-Maclaurin formula
Article copyright: © Copyright 1984 American Mathematical Society

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