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Fungrim entry: 90c66a

sinc(z)={(2z31z)sin(z)2cos(z)z2,z013,z=0\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:zCz \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
ComplexDerivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative
Sincsinc(z)\operatorname{sinc}(z) Sinc function
Powab{a}^{b} Power
Sinsin(z)\sin(z) Sine
Coscos(z)\cos(z) Cosine
CCC\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.

2020-08-27 09:56:25.682319 UTC