# 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

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

2019-12-30 15:00:46.909060 UTC