Fungrim home page

Fungrim entry: a4f9c9

n=01xn4=γ4+π49+2γ2π23+4γζ ⁣(3)\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
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...)
RiemannZetaζ ⁣(s)\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.

2020-08-27 09:56:25.682319 UTC