On a solution to the Basel problem based on the fundamental theorem of calculus

We give a proof of the identity \(\zeta(2)=\sum_{n=1}^\infty \frac{1}{n^2}=\frac{\pi^2}6\) using the fundamental theorem of calculus and differentiation under the integral sign.

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Bibliographic Details
Published in:arXiv.org 2021-04
Main Author: Alessio Del Vigna
Format: Article
Language:English
Subjects:
Calculus
Theorems
Online Access:Get full text
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Summary:We give a proof of the identity \(\zeta(2)=\sum_{n=1}^\infty \frac{1}{n^2}=\frac{\pi^2}6\) using the fundamental theorem of calculus and differentiation under the integral sign.
ISSN:2331-8422