Fungrim home page

Fungrim entry: 231141

limε0+λ ⁣(n+iε)={1,n even,n odd\lim_{\varepsilon \to {0}^{+}} \lambda\!\left(n + i \varepsilon\right) = \begin{cases} 1, & n \text{ even}\\-\infty, & n \text{ odd}\\ \end{cases}
Assumptions:nZn \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
RightLimitlimxa+f(x)\lim_{x \to {a}^{+}} f(x) Limiting value, from the right
ModularLambdaλ(τ)\lambda(\tau) Modular lambda function
ConstIii Imaginary unit
Infinity\infty Positive infinity
ZZZ\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