# Fungrim entry: 8f10b0

$\phi(q) = \sum_{k=-\infty}^{\infty} {\left(-1\right)}^{k} {q}^{k \left(3 k - 1\right) / 2}$
Assumptions:$q \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|q\right| < 1$
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
EulerQSeries$\phi(q)$ Euler's q-series
Sum$\sum_{n} f(n)$ Sum
Pow${a}^{b}$ Power
Infinity$\infty$ Positive infinity
CC$\mathbb{C}$ Complex numbers
Abs$\left|z\right|$ 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

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-08-27 09:56:25.682319 UTC