Abstract
TextIn this article, we study the nature of the forward shifted series σr=∑n>r|bn|n−r where r is a positive integer and bn are Bernoulli numbers of the second kind, expressing them in terms of the derivatives ζ′(−k) of zeta at the negative integers and Euler's constant γ. These expressions may be inverted to produce new series expansions for the quotient ζ(2k+1)/ζ(2k). Motivated by a theoretical interpretation of these series in terms of Ramanujan summation, we give an explicit formula for the Ramanujan sum of hyperharmonic numbers as an application of our results. VideoFor a video summary of this paper, please visit https://youtu.be/uyLmgDh9JVs.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.