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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1984-0736457-5
PII: S 0025-5718(1984)0736457-5
Keywords: Reciprocal gamma distribution, generating function, Euler-Maclaurin formula
Article copyright: © Copyright 1984 American Mathematical Society