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Fungrim entry: 39ce44

n=01xn3=γ3γπ224ζ ⁣(3)\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
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("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))))))

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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