Basel Problem

Artur Korniłowicz; Karol Pąk

doi:10.1515/forma-2017-0013

Basel Problem – Preliminaries

Formalized Mathematics ◽

10.1515/forma-2017-0013 ◽

2017 ◽

Vol 25 (2) ◽

pp. 141-147 ◽

Cited By ~ 1

Author(s):

Artur Korniłowicz ◽

Karol Pąk

Keyword(s):

Basel Problem

Summary In the article we formalize in the Mizar system [4] preliminary facts needed to prove the Basel problem [7, 1]. Facts that are independent from the notion of structure are included here.

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91.19 The Basel problem and the zeros of

The Mathematical Gazette ◽

10.1017/s002555720018115x ◽

2007 ◽

Vol 91 (520) ◽

pp. 120-123 ◽

Cited By ~ 1

Author(s):

Francis Woodhouse

Keyword(s):

Basel Problem

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Probabilistic Proofs of Euler Identities

Journal of Applied Probability ◽

10.1017/s0021900200013887 ◽

2013 ◽

Vol 50 (04) ◽

pp. 1206-1212 ◽

Cited By ~ 1

Author(s):

Lars Holst

Keyword(s):

Limit Theorem ◽

Probability Distribution ◽

Generating Function ◽

Local Limit Theorem ◽

Infinite Product ◽

Random Variables ◽

Local Limit ◽

Moment Generating Function ◽

Basel Problem

Formulae for ζ(2n) andLχ4(2n+ 1) involving Euler and tangent numbers are derived using the hyperbolic secant probability distribution and its moment generating function. In particular, the Basel problem, where ζ(2) = π2/ 6, is considered. Euler's infinite product for the sine is also proved using the distribution of sums of independent hyperbolic secant random variables and a local limit theorem.

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A Short and Elementary Proof of the Basel Problem

College Mathematics Journal ◽

10.4169/college.math.j.47.2.134 ◽

2016 ◽

Vol 47 (2) ◽

pp. 134-135 ◽

Cited By ~ 2

Author(s):

Samuel G. Moreno

Keyword(s):

Elementary Proof ◽

Basel Problem

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Formalized Mathematics ◽

10.1515/forma-2017-0014 ◽

2017 ◽

Vol 25 (2) ◽

pp. 149-155

Author(s):

Karol Pąk ◽

Artur Korniłowicz

Keyword(s):

Elementary Proof ◽

Link Type ◽

Basel Problem

Summary A rigorous elementary proof of the Basel problem [6, 1] $$\sum\nolimits_{n = 1}^\infty {{1 \over {n^2 }} = {{\pi ^2 } \over 6}} $$ is formalized in the Mizar system [3]. This theorem is item #14 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/.

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Is there a π solution for ∑i^{-i+1}

10.31219/osf.io/ax8dj ◽

2021 ◽

Author(s):

Alex Nguhi

Keyword(s):

Basel Problem

The sum∑i^{-i+1} converges very fast as compared with∑i^{-i}, but its value is very close to Euler's solution for the Basel Problem. This begs the question, can there be a solution involving π or other identities ?

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