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Fungrim entry: 599417

n=0p(n)qn=1ϕ(q)\sum_{n=0}^{\infty} p(n) {q}^{n} = \frac{1}{\phi(q)}
Assumptions:qCandq<1q \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left|q\right| < 1
TeX:
\sum_{n=0}^{\infty} p(n) {q}^{n} = \frac{1}{\phi(q)}

q \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left|q\right| < 1
Definitions:
Fungrim symbol Notation Short description
Sumnf(n)\sum_{n} f(n) Sum
PartitionsPp(n)p(n) Integer partition function
Powab{a}^{b} Power
Infinity\infty Positive infinity
EulerQSeriesϕ(q)\phi(q) Euler's q-series
CCC\mathbb{C} Complex numbers
Absz\left|z\right| Absolute value
Source code for this entry:
Entry(ID("599417"),
    Formula(Equal(Sum(Mul(PartitionsP(n), Pow(q, n)), For(n, 0, Infinity)), Div(1, EulerQSeries(q)))),
    Variables(q),
    Assumptions(And(Element(q, CC), Less(Abs(q), 1))))

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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