Fungrim home page

Fungrim entry: 9d666f

n=0Bnxn=k=0xkj=1k(1jx)\sum_{n=0}^{\infty} B_{n} {x}^{n} = \sum_{k=0}^{\infty} \frac{{x}^{k}}{\prod_{j=1}^{k} \left(1 - j x\right)}
Assumptions:x=0x = 0
\sum_{n=0}^{\infty} B_{n} {x}^{n} = \sum_{k=0}^{\infty} \frac{{x}^{k}}{\prod_{j=1}^{k} \left(1 - j x\right)}

x = 0
Fungrim symbol Notation Short description
Sumnf(n)\sum_{n} f(n) Sum
BellNumberBnB_{n} Bell number
Powab{a}^{b} Power
Infinity\infty Positive infinity
Productnf(n)\prod_{n} f(n) Product
Source code for this entry:
    Formula(Equal(Sum(Mul(BellNumber(n), Pow(x, n)), For(n, 0, Infinity)), Sum(Div(Pow(x, k), Product(Parentheses(Sub(1, Mul(j, x))), For(j, 1, k))), For(k, 0, Infinity)))),
    Assumptions(Equal(x, 0)))

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