# Fungrim entry: e96684

$\lambda\!\left(\tau\right) = 16 q \prod_{k=1}^{\infty} {\left(\frac{1 + {q}^{2 k}}{1 + {q}^{2 k - 1}}\right)}^{8}\; \text{ where } q = {e}^{\pi i \tau}$
Assumptions:$\tau \in \mathbb{H}$
TeX:
\lambda\!\left(\tau\right) = 16 q \prod_{k=1}^{\infty} {\left(\frac{1 + {q}^{2 k}}{1 + {q}^{2 k - 1}}\right)}^{8}\; \text{ where } q = {e}^{\pi i \tau}

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
ModularLambda$\lambda\!\left(\tau\right)$ Modular lambda function
Product$\prod_{n} f\!\left(n\right)$ Product
Pow${a}^{b}$ Power
Infinity$\infty$ Positive infinity
Exp${e}^{z}$ Exponential function
ConstPi$\pi$ The constant pi (3.14...)
ConstI$i$ Imaginary unit
HH$\mathbb{H}$ Upper complex half-plane
Source code for this entry:
Entry(ID("e96684"),
Formula(Equal(ModularLambda(tau), Where(Mul(Mul(16, q), Product(Pow(Div(Add(1, Pow(q, Mul(2, k))), Add(1, Pow(q, Sub(Mul(2, k), 1)))), 8), Tuple(k, 1, Infinity))), Equal(q, Exp(Mul(Mul(ConstPi, ConstI), tau)))))),
Variables(tau),
Assumptions(Element(tau, HH)))

## Topics using this entry

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

2019-09-19 20:12:49.583742 UTC