Fungrim home page

Fungrim entry: 1165fc

n=01xn2=γ2+π22\sum_{n=0}^{\infty} \frac{1}{x_{n}^{2}} = {\gamma}^{2} + \frac{{\pi}^{2}}{2}
TeX:
\sum_{n=0}^{\infty} \frac{1}{x_{n}^{2}} = {\gamma}^{2} + \frac{{\pi}^{2}}{2}
Definitions:
Fungrim symbol Notation Short description
Sumnf(n)\sum_{n} f(n) Sum
Powab{a}^{b} Power
DigammaFunctionZeroxnx_{n} Zero of the digamma function
Infinity\infty Positive infinity
ConstGammaγ\gamma The constant gamma (0.577...)
Piπ\pi The constant pi (3.14...)
Source code for this entry:
Entry(ID("1165fc"),
    Formula(Equal(Sum(Div(1, Pow(DigammaFunctionZero(n), 2)), For(n, 0, Infinity)), Add(Pow(ConstGamma, 2), Div(Pow(Pi, 2), 2)))))

Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-08-27 09:56:25.682319 UTC