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Extensions of an identity of Euler
Published online by Cambridge University Press: 18 June 2020
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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.
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- © Mathematical Association 2020