Fungrim entry: 8f10b0

\phi\!\left(q\right) = \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| \lt 1

TeX:

\phi\!\left(q\right) = \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| \lt 1

Definitions:

Fungrim symbol	Notation	Short description
`EulerQSeries`	$\phi\!\left(q\right)$	Euler's q-series
`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))), Tuple(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.

2019-06-18 07:49:59.356594 UTC