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February 2021 Two integrals involving the Legendre chi function
Anthony Sofo
Rocky Mountain J. Math. 51(1): 295-314 (February 2021). DOI: 10.1216/rmj.2021.51.295

Abstract

We investigate the representations of integrals involving the product of the Legendre-chi function and the tanh1x or arctanx functions. The investigation will show that in many cases these integrals take an explicit form involving the Riemann zeta function, the Dirichlet eta function, Dirichlet lambda function and many other special functions. Some examples illustrating the theorems will be detailed.

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Anthony Sofo. "Two integrals involving the Legendre chi function." Rocky Mountain J. Math. 51 (1) 295 - 314, February 2021. https://doi.org/10.1216/rmj.2021.51.295

Information

Received: 31 May 2020; Revised: 16 August 2020; Accepted: 16 August 2020; Published: February 2021
First available in Project Euclid: 28 May 2021

Digital Object Identifier: 10.1216/rmj.2021.51.295

Subjects:
Primary: 11M06 , 11M35 , 26B15
Secondary: 11Y60 , 33B15

Keywords: Dirichlet beta functions , Dirichlet lambda function , Euler sums , hyperbolic function , Legendre chi function , trigonometric function , zeta functions

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.51 • No. 1 • February 2021
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