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

Specific values of the digamma function