Fungrim entry: 231141

\lim_{\varepsilon \to {0}^{+}} \lambda\!\left(n + i \varepsilon\right) = \begin{cases} 1, & n \text{ even}\\-\infty, & n \text{ odd}\\ \end{cases}

Assumptions:

n \in \mathbb{Z}

TeX:

\lim_{\varepsilon \to {0}^{+}} \lambda\!\left(n + i \varepsilon\right) = \begin{cases} 1, & n \text{ even}\\-\infty, & n \text{ odd}\\ \end{cases}

n \in \mathbb{Z}

Definitions:

Fungrim symbol	Notation	Short description
`RightLimit`	$\lim_{x \to {a}^{+}} f(x)$	Limiting value, from the right
`ModularLambda`	$\lambda(\tau)$	Modular lambda function
`ConstI`	$i$	Imaginary unit
`Infinity`	$\infty$	Positive infinity
`ZZ`	$\mathbb{Z}$	Integers

Source code for this entry:

Entry(ID("231141"),
    Formula(Equal(RightLimit(ModularLambda(Add(n, Mul(ConstI, epsilon))), For(epsilon, 0)), Cases(Tuple(1, Even(n)), Tuple(Neg(Infinity), Odd(n))))),
    Variables(n),
    Assumptions(Element(n, ZZ)))

Topics using this entry

Modular lambda 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