Extensions of an identity of Euler Journal Articles

abstract

• In this paper we state the original identity proved by Euler, and we provide an alternative proof of this result. We then extend the approach to derive a further identity for the sum of reciprocals of squares, along with two other related identities. We conclude by obtaining yet another extension of the identity, and this is accomplished by means of a probability density function, or pdf.

authors

• Brown, Geoffrey
• Balakrishnan, Narayanaswamy

status

• published 

publication date

• July 2020

has subject area

• 0101 Pure Mathematics (FoR)

published in

• Mathematical Gazette  Journal

keywords

• Mathematics
• Physical Sciences
• Science & Technology

Digital Object Identifier (DOI)

• 10.1017/mag.2020.46

start page

• 241

end page

• 246

volume

• 104

issue

• 560