Fungrim entry: 39ce44

\sum_{n=0}^{\infty} \frac{1}{x_{n}^{3}} = -{\gamma}^{3} - \frac{\gamma {\pi}^{2}}{2} - 4 \zeta\!\left(3\right)

TeX:

\sum_{n=0}^{\infty} \frac{1}{x_{n}^{3}} = -{\gamma}^{3} - \frac{\gamma {\pi}^{2}}{2} - 4 \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("39ce44"),
    Formula(Equal(Sum(Div(1, Pow(DigammaFunctionZero(n), 3)), For(n, 0, Infinity)), Sub(Sub(Neg(Pow(ConstGamma, 3)), Div(Mul(ConstGamma, Pow(Pi, 2)), 2)), Mul(4, RiemannZeta(3))))))

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