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

Dedekind eta function

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

2021-03-15 19:12:00.328586 UTC