# Fungrim entry: 921f34

$\lambda(\tau) = 16 q - 128 {q}^{2} + 704 {q}^{3} - 3072 {q}^{4} + 11488 {q}^{5} - 38400 {q}^{6} + \ldots \; \text{ where } q = {e}^{\pi i \tau}$
Assumptions:$\tau \in \mathbb{H}$
References:
• https://oeis.org/A115977
TeX:
\lambda(\tau) = 16 q - 128 {q}^{2} + 704 {q}^{3} - 3072 {q}^{4} + 11488 {q}^{5} - 38400 {q}^{6} + \ldots \; \text{ where } q = {e}^{\pi i \tau}

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
ModularLambda$\lambda(\tau)$ Modular lambda function
Pow${a}^{b}$ Power
Exp${e}^{z}$ Exponential function
Pi$\pi$ The constant pi (3.14...)
ConstI$i$ Imaginary unit
HH$\mathbb{H}$ Upper complex half-plane
Source code for this entry:
Entry(ID("921f34"),
Formula(EqualQSeriesEllipsis(ModularLambda(tau), tau, q, Sub(Add(Sub(Add(Sub(Mul(16, q), Mul(128, Pow(q, 2))), Mul(704, Pow(q, 3))), Mul(3072, Pow(q, 4))), Mul(11488, Pow(q, 5))), Mul(38400, Pow(q, 6))), Equal(q, Exp(Mul(Mul(Pi, ConstI), tau))))),
Variables(tau),
Assumptions(Element(tau, HH)),
References("https://oeis.org/A115977"))

## Topics using this entry

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