Definite Integral of Arctangent and Polylogarithmic Functions Expressed as a Series

Robert Reynolds and Allan Stauffer
Additional contact information
Robert Reynolds: Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada
Allan Stauffer: Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada

Mathematics, 2019, vol. 7, issue 11, 1-7

Abstract: We present a method using contour integration to evaluate the definite integral of arctangent reciprocal logarithmic integrals in terms of infinite sums. In a similar manner, we evaluate the definite integral involving the polylogarithmic function L i k ( y ) in terms of special functions. In various cases, these generalizations give the value of known mathematical constants such as Catalan’s constant G , Aprey’s constant ζ ( 3 ) , the Glaisher–Kinkelin constant A , l o g ( 2 ) , and π .

Keywords: Catalan; zeta; logarithm tangent function; Lerch function; polylogarithmic function; Glaisher–Kinkelin constant; contour integration (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/11/1099/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/11/1099/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:11:p:1099-:d:286682

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().