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Fungrim entry: 8f10b0

ϕ(q)=k=(1)kqk(3k1)/2\phi(q) = \sum_{k=-\infty}^{\infty} {\left(-1\right)}^{k} {q}^{k \left(3 k - 1\right) / 2}
Assumptions:qCandq<1q \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left|q\right| < 1
TeX:
\phi(q) = \sum_{k=-\infty}^{\infty} {\left(-1\right)}^{k} {q}^{k \left(3 k - 1\right) / 2}

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
Sumnf(n)\sum_{n} f(n) Sum
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("8f10b0"),
    Formula(Equal(EulerQSeries(q), Sum(Mul(Pow(-1, k), Pow(q, Div(Mul(k, Sub(Mul(3, k), 1)), 2))), For(k, Neg(Infinity), Infinity)))),
    Variables(q),
    Assumptions(And(Element(q, CC), Less(Abs(q), 1))))

Topics using this entry

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2019-10-05 13:11:19.856591 UTC