Fungrim entry: 50f72f

\operatorname{sinc}'(z) = -\frac{z}{3} \,{}_0F_1\!\left(\frac{5}{2}, -\frac{{z}^{2}}{4}\right)

Assumptions:

z \in \mathbb{C}

TeX:

\operatorname{sinc}'(z) = -\frac{z}{3} \,{}_0F_1\!\left(\frac{5}{2}, -\frac{{z}^{2}}{4}\right)

z \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`Derivative`	$\frac{d}{d z}\, f\!\left(z\right)$	Derivative
`Sinc`	$\operatorname{sinc}(z)$	Sinc function
`Hypergeometric0F1`	$\,{}_0F_1\!\left(a, z\right)$	Confluent hypergeometric limit function
`Pow`	${a}^{b}$	Power
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("50f72f"),
    Formula(Equal(Derivative(Sinc(z), For(z, z)), Neg(Mul(Div(z, 3), Hypergeometric0F1(Div(5, 2), Neg(Div(Pow(z, 2), 4))))))),
    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