# Fungrim entry: b7174d

$\tau = i \frac{K\!\left(1 - \lambda(\tau)\right)}{K\!\left(\lambda(\tau)\right)}$
Assumptions:$\tau \in \operatorname{Interior}(\mathcal{F}_{\lambda}) \cup \left\{ \tau : \tau \in \mathbb{H} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(\tau) = 1 \right\}$
TeX:
\tau = i \frac{K\!\left(1 - \lambda(\tau)\right)}{K\!\left(\lambda(\tau)\right)}

\tau \in \operatorname{Interior}(\mathcal{F}_{\lambda}) \cup \left\{ \tau : \tau \in \mathbb{H} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(\tau) = 1 \right\}
Definitions:
Fungrim symbol Notation Short description
ConstI$i$ Imaginary unit
EllipticK$K(m)$ Legendre complete elliptic integral of the first kind
ModularLambda$\lambda(\tau)$ Modular lambda function
ModularLambdaFundamentalDomain$\mathcal{F}_{\lambda}$ Fundamental domain of the modular lambda function
HH$\mathbb{H}$ Upper complex half-plane
Re$\operatorname{Re}(z)$ Real part
Source code for this entry:
Entry(ID("b7174d"),
Formula(Equal(tau, Mul(ConstI, Div(EllipticK(Sub(1, ModularLambda(tau))), EllipticK(ModularLambda(tau)))))),
Variables(tau),
Assumptions(Element(tau, Union(Interior(ModularLambdaFundamentalDomain), Set(tau, For(tau), And(Element(tau, HH), Equal(Re(tau), 1)))))))

## 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