Fungrim entry: 1165fc

\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
`Sum`	$\sum_{n} f(n)$	Sum
`Pow`	${a}^{b}$	Power
`DigammaFunctionZero`	$x_{n}$	Zero of the digamma function
`Infinity`	$\infty$	Positive infinity
`ConstGamma`	$\gamma$	The constant gamma (0.577...)
`Pi`	$\pi$	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

Specific values of the digamma function

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

2021-03-15 19:12:00.328586 UTC