Fungrim entry: 5ce30b

\psi^{(m)}\!\left(\frac{1}{2}\right) = {\left(-1\right)}^{m + 1} \left({2}^{m + 1} - 1\right) m ! \zeta\!\left(m + 1\right)

Assumptions:

m \in \mathbb{Z}_{\ge 1}

TeX:

\psi^{(m)}\!\left(\frac{1}{2}\right) = {\left(-1\right)}^{m + 1} \left({2}^{m + 1} - 1\right) m ! \zeta\!\left(m + 1\right)

m \in \mathbb{Z}_{\ge 1}

Definitions:

Fungrim symbol	Notation	Short description
`DigammaFunction`	$\psi\!\left(z\right)$	Digamma function
`Pow`	${a}^{b}$	Power
`Factorial`	$n !$	Factorial
`RiemannZeta`	$\zeta\!\left(s\right)$	Riemann zeta function
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n

Source code for this entry:

Entry(ID("5ce30b"),
    Formula(Equal(DigammaFunction(Div(1, 2), m), Mul(Mul(Mul(Pow(-1, Add(m, 1)), Sub(Pow(2, Add(m, 1)), 1)), Factorial(m)), RiemannZeta(Add(m, 1))))),
    Variables(m),
    Assumptions(Element(m, ZZGreaterEqual(1))))

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