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
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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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 M. Abramowitz and I.A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables. National Bureau of Standards Applied Mathematics Series, 55, U.S. Government Printing Office, Washington, D.C., 1964. MR 0167642 (29:4914)
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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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 O. Oloa, Some Eulertype integrals and a new rational series for Euler's constant, ``Tapas in Experimental Mathematics'' (T. Amdeberhan and V. Moll, eds.), Contemporary Mathematics, vol. 457, Amer. Math. Soc., Providence, RI, 2008, 253264. MR 2427676
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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
PII:
S 00029939(09)101570
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.
