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Fungrim entry: 9d666f

∑n=0∞Bnxn=∑k=0∞xk∏j=1k(1−jx)\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
TeX:
\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
Definitions:
Fungrim symbol Notation Short description
Sum∑nf(n)\sum_{n} f(n) Sum
BellNumberBnB_{n} Bell number
Powab{a}^{b} Power
Infinity∞\infty Positive infinity
Product∏nf(n)\prod_{n} f(n) Product
Source code for this entry:
Entry(ID("9d666f"),
    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)))),
    Variables(x),
    Assumptions(Equal(x, 0)))

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2021-03-15 19:12:00.328586 UTC