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Fungrim entry: 2e7fdb

ϕ(q)=k=1(1qk)\phi(q) = \prod_{k=1}^{\infty} \left(1 - {q}^{k}\right)
Assumptions:qCandq<1q \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left|q\right| < 1
TeX:
\phi(q) = \prod_{k=1}^{\infty} \left(1 - {q}^{k}\right)

q \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left|q\right| < 1
Definitions:
Fungrim symbol Notation Short description
EulerQSeriesϕ(q)\phi(q) Euler's q-series
Productnf(n)\prod_{n} f(n) Product
Powab{a}^{b} Power
Infinity\infty Positive infinity
CCC\mathbb{C} Complex numbers
Absz\left|z\right| Absolute value
Source code for this entry:
Entry(ID("2e7fdb"),
    Formula(Equal(EulerQSeries(q), Product(Parentheses(Sub(1, Pow(q, k))), For(k, 1, Infinity)))),
    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