Fungrim entry: b1a2e1

\zeta\!\left(s\right) = \frac{1}{s - 1} + \sum_{n=0}^{\infty} \frac{{\left(-1\right)}^{n}}{n !} \gamma_{n} {\left(s - 1\right)}^{n}

Assumptions:

s \in \mathbb{C}

TeX:

\zeta\!\left(s\right) = \frac{1}{s - 1} + \sum_{n=0}^{\infty} \frac{{\left(-1\right)}^{n}}{n !} \gamma_{n} {\left(s - 1\right)}^{n}

s \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`RiemannZeta`	$\zeta\!\left(s\right)$	Riemann zeta function
`Sum`	$\sum_{n} f(n)$	Sum
`Pow`	${a}^{b}$	Power
`Factorial`	$n !$	Factorial
`StieltjesGamma`	$\gamma_{n}\!\left(a\right)$	Stieltjes constant
`Infinity`	$\infty$	Positive infinity
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("b1a2e1"),
    Formula(Equal(RiemannZeta(s), Add(Div(1, Sub(s, 1)), Sum(Mul(Mul(Div(Pow(-1, n), Factorial(n)), StieltjesGamma(n)), Pow(Sub(s, 1), n)), For(n, 0, Infinity))))),
    Variables(s),
    Assumptions(Element(s, CC)))

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