Volume 22 (2) 2016, 103-108
Some Remarks on Glaisher-Ramanujan Type Integrals
Patkowski Alexander 1, Wolf Marek 2
1 1390 Bumps River Rd. Centerville, MA 02632,
USA E-mail: email@example.com
2 Cardinal Stefan Wyszynski University
Faculty of Mathematics and Natural Sciences. College of Sciences ul. Wóycickiego 1/3, Auditorium Maximum, (room 113) PL-01-938 Warsaw, Poland
Received: 06 February 2016; revised: 23 May 2016 ; accepted: 24 May 2016 ; published online: 08 June 2016
Some integrals of the Glaisher-Ramanujan type are established in a more general form than in previous studies. As an application we prove some Ramanujan-type series identities, as well as a new formula for the Dirichlet beta function at the value s = 3. We also present a Mathematica program calculating values of beta function at odd positive arguments.
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