Fungrim entry: 90c66a

$\operatorname{sinc}''(z) = \begin{cases} \left(\frac{2}{{z}^{3}} - \frac{1}{z}\right) \sin(z) - \frac{2 \cos(z)}{{z}^{2}}, & z \ne 0\\-\frac{1}{3}, & z = 0\\ \end{cases}$
Assumptions:$z \in \mathbb{C}$
TeX:
\operatorname{sinc}''(z) = \begin{cases} \left(\frac{2}{{z}^{3}} - \frac{1}{z}\right) \sin(z) - \frac{2 \cos(z)}{{z}^{2}}, & z \ne 0\\-\frac{1}{3}, & 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
Pow${a}^{b}$ Power
Sin$\sin(z)$ Sine
Cos$\cos(z)$ Cosine
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("90c66a"),
Formula(Equal(ComplexDerivative(Sinc(z), For(z, z, 2)), Cases(Tuple(Sub(Mul(Sub(Div(2, Pow(z, 3)), Div(1, z)), Sin(z)), Div(Mul(2, Cos(z)), Pow(z, 2))), NotEqual(z, 0)), Tuple(Neg(Div(1, 3)), 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