The Laplace transform of the psi function
Author:
Atul Dixit
Journal:
Proc. Amer. Math. Soc. 138 (2010), 593603
MSC (2000):
Primary 33B15
Published electronically:
September 25, 2009
MathSciNet review:
2557176
Fulltext PDF Free Access
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Abstract: An expression for the Laplace transform of the psi function is derived using two different methods. It is then applied to evaluate the definite integral for and to resolve a conjecture posed by Olivier Oloa.
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 T. Amdeberhan, O. Espinosa and V.H. Moll, The Laplace transform of the digamma function: An integral due to Glasser, Manna and Oloa, Proc. Amer. Math. Soc., 136 (2008) 32113221. MR 2407086 (2009d:33005)
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 O. Espinosa and V.H. Moll, On some integrals involving the Hurwitz zeta function. Part I, The Ramanujan Journal, 6 (2002) 159188. MR 1908196 (2003f:11127)
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Additional Information
Atul Dixit
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801
Email:
aadixit2@illinois.edu
DOI:
http://dx.doi.org/10.1090/S0002993909101570
Keywords:
Laplace transform,
gamma function,
psi function.
Received by editor(s):
October 28, 2008
Published electronically:
September 25, 2009
Communicated by:
Peter A. Clarkson
Article copyright:
© Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
