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
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
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M. G. Kendall & A. Stuart, The Advanced Theory of Statistics, Vol. I, Charles Griffin & Company Limited, 1958.
D. F. Kerridge & G. W. Cook, "Yet another series for the normal integral," Biometrika, v. 63, 1976, pp. 401-403.
- Arne Fransén and Staffan Wrigge, Calculation of the moments and the moment generating function for the reciprocal gamma distribution, Math. Comp. 42 (1984), no. 166, 601–616. MR 736456, DOI 10.1090/S0025-5718-1984-0736456-3
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Math. Comp. 42 (1984), 617-621
- MSC: Primary 65D20; Secondary 60E10, 62E15, 65U05
- DOI: https://doi.org/10.1090/S0025-5718-1984-0736457-5
- MathSciNet review: 736457