Open AccessEVALUATING LOG-TANGENT INTEGRALS VIA EULER SUMS
Author(s) -
Anthony Sofo
Publication year - 2022
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/mma.2022.13100
Subject(s) - mathematics , riemann zeta function , logarithm , inverse trigonometric functions , euler's formula , tangent , pure mathematics , function (biology) , riemann hypothesis , dirichlet distribution , representation (politics) , gamma function , hyperbolic function , mathematical analysis , geometry , evolutionary biology , politics , political science , law , biology , boundary value problem
An investigation into the representation of integrals involving the product of the logarithm and the arctan functions, reducing to log-tangent integrals, will be undertaken in this paper. We 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.