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Fungrim entry: 522b04

zez1=n=0Bnznn!\frac{z}{{e}^{z} - 1} = \sum_{n=0}^{\infty} B_{n} \frac{{z}^{n}}{n !}
Assumptions:zC  and  z<2π  and  z0z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|z\right| < 2 \pi \;\mathbin{\operatorname{and}}\; z \ne 0
\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
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
Piπ\pi The constant pi (3.14...)
Source code for this entry:
    Formula(Equal(Div(z, Sub(Exp(z), 1)), Sum(Mul(BernoulliB(n), Div(Pow(z, n), Factorial(n))), For(n, 0, Infinity)))),
    Assumptions(And(Element(z, CC), Less(Abs(z), Mul(2, Pi)), NotEqual(z, 0))))

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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