Generalization of the Glasser - Manna - Oloa integral and some new integrals of similar type

Details Generalization of the Glasser - Manna - Oloa integral and some new integrals of similar type Generalization of the Glasser - Manna - Oloa integral and some new integrals of similar type

2010-07-20

arxiv.org/abs/1007.3460v1

Mathematics

Classical Analysis and ODEs

8 pages

Scientific paper

As was shown in the previous works by other authors, Glasser - Manna - Oloa integral arise in the study of the Laplace transform of the dilogarithm function and can be evaluated in a closed form. In this article, we give a one parametric generalization of the Glasser - Manna - Oloa integral. The method employed in the course of derivation allows to obtain some new integrals of similar type. These include also integral representation of the Hurwitz zeta function and some beautiful formulae involving the logarithm of the gamma function of the argument -ix+ln(2cosx).

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