Abstract
In this paper the countable family of generalized Gregory’s series (all of which are the power series having the radius of convergence equal to one) is defined. Sums Sn(x),n=1,2,… of these series are found – first in the definite integral form and next in the form of finite linear combination of arcus tangents of some linear forms of x. It enables to extend the definition of Sn(x) for all x∈C⧹-12n for every n∈N. Moreover, for new functions Sn(x), obtained in result of this extension, many fundamental and surprising integral and trigonometric identities are received. Sums of the series of differences of odd harmonic numbers are presented as well.
Sign-in/Register to access full text options 
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.
