Fungrim entry: 2e7fdb

\phi(q) = \prod_{k=1}^{\infty} \left(1 - {q}^{k}\right)

Assumptions:

q \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
`EulerQSeries`	$\phi(q)$	Euler's q-series
`Product`	$\prod_{n} f(n)$	Product
`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("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))))

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