Fungrim home page

Fungrim entry: b1a2e1

ζ ⁣(s)=1s1+n=0(1)nn!γn(s1)n\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:sCs \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
RiemannZetaζ ⁣(s)\zeta\!\left(s\right) Riemann zeta function
Sumnf(n)\sum_{n} f(n) Sum
Powab{a}^{b} Power
Factorialn!n ! Factorial
StieltjesGammaγn ⁣(a)\gamma_{n}\!\left(a\right) Stieltjes constant
Infinity\infty Positive infinity
CCC\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.

2020-08-27 09:56:25.682319 UTC