A338106 Decimal expansion of Sum_{m>1, n>1} 1/(m^2*n^2-1).
4, 2, 3, 0, 3, 5, 5, 2, 5, 7, 6, 1, 3, 1, 3, 1, 5, 9, 7, 4, 2, 0, 9, 7, 1, 0, 1, 6, 3, 9, 1, 0, 3, 8, 6, 2, 8, 9, 9, 5, 4, 6, 4, 9, 7, 0, 7, 0, 2, 9, 1, 0, 7, 8, 9, 3, 5, 7, 5, 2, 3, 2, 5, 1, 6, 5, 5, 0, 4, 5, 9, 1, 2, 7, 0, 4, 5, 5, 3, 5, 4, 8, 0, 2, 4, 8, 1, 2
Offset: 0
Examples
0.4230355257613131597420971016391038628995464... (with help of _Amiram Eldar_).
References
- Jean-Marie Monier, Analyse, Exercices corrigés, 2ème année MP, Dunod, 1997, Exercice 3.25, p. 277.
Programs
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Mathematica
RealDigits[Sum[(Zeta[2*k] - 1)^2, {k, 1, 100}], 10, 90][[1]] (* Amiram Eldar, Oct 10 2020 *) -
PARI
sumpos(k=1, (zeta(2*k) - 1)^2) \\ Michel Marcus, Oct 10 2020
Formula
Equals Sum_{k>0} (zeta(2*k) - 1)^2.
Equals -3/4 + Sum_{k>=2} (1/2 - Pi*cot(Pi/k)/(2*k)). - Vaclav Kotesovec, Oct 14 2020
Comments