Fungrim entry: 768c77

$\operatorname{sinc}'(z) = \begin{cases} \frac{\cos(z)}{z} - \frac{\sin(z)}{{z}^{2}}, & z \ne 0\\0, & z = 0\\ \end{cases}$
Assumptions:$z \in \mathbb{C}$
TeX:
\operatorname{sinc}'(z) = \begin{cases} \frac{\cos(z)}{z} - \frac{\sin(z)}{{z}^{2}}, & z \ne 0\\0, & z = 0\\ \end{cases}

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
ComplexDerivative$\frac{d}{d z}\, f\!\left(z\right)$ Complex derivative
Sinc$\operatorname{sinc}(z)$ Sinc function
Cos$\cos(z)$ Cosine
Sin$\sin(z)$ Sine
Pow${a}^{b}$ Power
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("768c77"),
Formula(Equal(ComplexDerivative(Sinc(z), For(z, z)), Cases(Tuple(Sub(Div(Cos(z), z), Div(Sin(z), Pow(z, 2))), NotEqual(z, 0)), Tuple(0, Equal(z, 0))))),
Variables(z),
Assumptions(Element(z, CC)))

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