Fungrim home page

Fungrim entry: 4b20ab

{λ ⁣(τ):τHandRe ⁣(τ)=1}=(,0)\left\{ \lambda\!\left(\tau\right) : \tau \in \mathbb{H} \,\mathbin{\operatorname{and}}\, \operatorname{Re}\!\left(\tau\right) = -1 \right\} = \left(-\infty, 0\right)
This mapping is one-to-one.
References:
  • J. M. Borwein and P. B. Borwein. Pi and the AGM. Wiley, New York, 1987. p. 118.
TeX:
\left\{ \lambda\!\left(\tau\right) : \tau \in \mathbb{H} \,\mathbin{\operatorname{and}}\, \operatorname{Re}\!\left(\tau\right) = -1 \right\} = \left(-\infty, 0\right)
Definitions:
Fungrim symbol Notation Short description
SetBuilder{f ⁣(x):P ⁣(x)}\left\{ f\!\left(x\right) : P\!\left(x\right) \right\} Set comprehension
ModularLambdaλ ⁣(τ)\lambda\!\left(\tau\right) Modular lambda function
HHH\mathbb{H} Upper complex half-plane
ReRe ⁣(z)\operatorname{Re}\!\left(z\right) Real part
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity\infty Positive infinity
Source code for this entry:
Entry(ID("4b20ab"),
    Formula(Equal(SetBuilder(ModularLambda(tau), tau, And(Element(tau, HH), Equal(Re(tau), -1))), OpenInterval(Neg(Infinity), 0))),
    Description("This mapping is one-to-one."),
    References("J. M. Borwein and P. B. Borwein. Pi and the AGM. Wiley, New York, 1987. p. 118."))

Topics using this entry

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

2019-09-15 14:14:26.267625 UTC