# 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