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Fungrim entry: 768c77

sinc(z)={cos(z)zsin(z)z2,z00,z=0\operatorname{sinc}'(z) = \begin{cases} \frac{\cos(z)}{z} - \frac{\sin(z)}{{z}^{2}}, & z \ne 0\\0, & z = 0\\ \end{cases}
Assumptions:zCz \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
ComplexDerivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative
Sincsinc(z)\operatorname{sinc}(z) Sinc function
Coscos(z)\cos(z) Cosine
Sinsin(z)\sin(z) Sine
Powab{a}^{b} Power
CCC\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)))

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2020-08-27 09:56:25.682319 UTC