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

Sinc 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