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

Sinc function