Fungrim home page

Fungrim entry: 522b04

zez1=n=0Bnznn!\frac{z}{{e}^{z} - 1} = \sum_{n=0}^{\infty} B_{n} \frac{{z}^{n}}{n !}
Assumptions:zCandz<2πandz0z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left|z\right| < 2 \pi \,\mathbin{\operatorname{and}}\, z \ne 0
TeX:
\frac{z}{{e}^{z} - 1} = \sum_{n=0}^{\infty} B_{n} \frac{{z}^{n}}{n !}

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left|z\right| < 2 \pi \,\mathbin{\operatorname{and}}\, z \ne 0
Definitions:
Fungrim symbol Notation Short description
Expez{e}^{z} Exponential function
Sumnf(n)\sum_{n} f(n) Sum
BernoulliBBnB_{n} Bernoulli number
Powab{a}^{b} Power
Factorialn!n ! Factorial
Infinity\infty Positive infinity
CCC\mathbb{C} Complex numbers
Absz\left|z\right| Absolute value
ConstPiπ\pi The constant pi (3.14...)
Source code for this entry:
Entry(ID("522b04"),
    Formula(Equal(Div(z, Sub(Exp(z), 1)), Sum(Mul(BernoulliB(n), Div(Pow(z, n), Factorial(n))), For(n, 0, Infinity)))),
    Variables(z),
    Assumptions(And(Element(z, CC), Less(Abs(z), Mul(2, ConstPi)), Unequal(z, 0))))

Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-10-05 13:11:19.856591 UTC