# Fungrim entry: f4fd7d

$\left|\operatorname{sinc}\!\left({e}^{i \theta} \infty\right)\right| = \lim_{x \to \infty} \left|\operatorname{sinc}\!\left({e}^{i \theta} x\right)\right| = \begin{cases} 0, & {e}^{i \theta} \in \left\{-1, 1\right\}\\\infty, & \text{otherwise}\\ \end{cases}$
Assumptions:$\theta \in \mathbb{R}$
TeX:
\left|\operatorname{sinc}\!\left({e}^{i \theta} \infty\right)\right| = \lim_{x \to \infty} \left|\operatorname{sinc}\!\left({e}^{i \theta} x\right)\right| = \begin{cases} 0, & {e}^{i \theta} \in \left\{-1, 1\right\}\\\infty, & \text{otherwise}\\ \end{cases}

\theta \in \mathbb{R}
Definitions:
Fungrim symbol Notation Short description
Abs$\left|z\right|$ Absolute value
Sinc$\operatorname{sinc}(z)$ Sinc function
Exp${e}^{z}$ Exponential function
ConstI$i$ Imaginary unit
Infinity$\infty$ Positive infinity
RealLimit$\lim_{x \to a} f(x)$ Limiting value, real variable
RR$\mathbb{R}$ Real numbers
Source code for this entry:
Entry(ID("f4fd7d"),
Formula(Equal(Abs(Sinc(Mul(Exp(Mul(ConstI, theta)), Infinity))), RealLimit(Abs(Sinc(Mul(Exp(Mul(ConstI, theta)), x))), For(x, Infinity)), Cases(Tuple(0, Element(Exp(Mul(ConstI, theta)), Set(-1, 1))), Tuple(Infinity, Otherwise)))),
Variables(theta),
Assumptions(Element(theta, RR)))

## 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