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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Integrals of powers of loggamma


Authors: Tewodros Amdeberhan, Mark W. Coffey, Olivier Espinosa, Christoph Koutschan, Dante V. Manna and Victor H. Moll
Journal: Proc. Amer. Math. Soc. 139 (2011), 535-545
MSC (2010): Primary 33B15
Published electronically: August 18, 2010
MathSciNet review: 2736336
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Abstract: Properties of the integral of powers of $ \log \Gamma(x)$ from 0 to $ 1$ are considered. Analytic evaluations for the first two powers are presented. Empirical evidence for the cubic case is discussed.


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Additional Information

Tewodros Amdeberhan
Affiliation: Department of Mathematics, Tulane University, New Orleans, Louisiana 70118
Email: tamdeberhan@math.tulane.edu

Mark W. Coffey
Affiliation: Department of Physics, Colorado School of Mines, Golden, Colorado 80401
Email: mcoffey@mines.edu

Olivier Espinosa
Affiliation: Departmento de Fisica, Universidad Santa Maria, Valparaiso, Chile
Email: olivier.espinosa@usm.cl

Christoph Koutschan
Affiliation: Department of Mathematics, Tulane University, New Orleans, Louisiana 70118
Email: ckoutsch@tulane.edu

Dante V. Manna
Affiliation: Department of Mathematics and Computer Science, Virginia Wesleyan College, Norfolk, Virginia 23502
Email: dmanna@vwc.edu

Victor H. Moll
Affiliation: Department of Mathematics, Tulane University, New Orleans, Louisiana 70118
Email: vhm@math.tulane.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10589-0
PII: S 0002-9939(2010)10589-0
Keywords: Integrals, transformations, loggamma, Hurwitz zeta function
Received by editor(s): February 23, 2010
Received by editor(s) in revised form: March 8, 2010
Published electronically: August 18, 2010
Communicated by: Ken Ono
Article copyright: © Copyright 2010 American Mathematical Society