# Fungrim entry: a4f9c9

$\sum_{n=0}^{\infty} \frac{1}{x_{n}^{4}} = {\gamma}^{4} + \frac{{\pi}^{4}}{9} + \frac{2 {\gamma}^{2} {\pi}^{2}}{3} + 4 \gamma \zeta\!\left(3\right)$
TeX:
\sum_{n=0}^{\infty} \frac{1}{x_{n}^{4}} = {\gamma}^{4} + \frac{{\pi}^{4}}{9} + \frac{2 {\gamma}^{2} {\pi}^{2}}{3} + 4 \gamma \zeta\!\left(3\right)
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...)
RiemannZeta$\zeta\!\left(s\right)$ Riemann zeta function
Source code for this entry:
Entry(ID("a4f9c9"),
Formula(Equal(Sum(Div(1, Pow(DigammaFunctionZero(n), 4)), For(n, 0, Infinity)), Add(Add(Add(Pow(ConstGamma, 4), Div(Pow(Pi, 4), 9)), Div(Mul(Mul(2, Pow(ConstGamma, 2)), Pow(Pi, 2)), 3)), Mul(4, Mul(ConstGamma, RiemannZeta(3)))))))

## Topics using this entry

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