Abstract
We evaluate the following family of logarithmic integrals in closed form:12π∫02π|1+reit|2nlogm|1+reit|dt for n∈Z⩾0 and m=0,1,2,3,4, r∈[−1,1]. In 1995, Shen conducted evaluations for specific instances where r equals −1 with n equal to 0, as well as when m assumes the values 1, 2, 3, and 4. Moreover, by employing these integrals, we derive generating functions for certain sequences that incorporate harmonic numbers and binomial coefficients. Furthermore, we assess a selection of series that encompass squared central binomial coefficients and harmonic numbers.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
