Fungrim entry: 1c3766

${\operatorname{sinc}}^{(n)}(0) = \begin{cases} {\left(-1\right)}^{\left\lfloor n / 2 \right\rfloor} \frac{1}{n + 1}, & n \text{ even}\\0, & n \text{ odd}\\ \end{cases}$
Assumptions:$n \in \mathbb{Z}_{\ge 0}$
TeX:
{\operatorname{sinc}}^{(n)}(0) = \begin{cases} {\left(-1\right)}^{\left\lfloor n / 2 \right\rfloor} \frac{1}{n + 1}, & n \text{ even}\\0, & n \text{ odd}\\ \end{cases}

n \in \mathbb{Z}_{\ge 0}
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
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Source code for this entry:
Entry(ID("1c3766"),
Formula(Equal(ComplexDerivative(Sinc(z), For(z, 0, n)), Cases(Tuple(Mul(Pow(-1, Floor(Div(n, 2))), Div(1, Add(n, 1))), Even(n)), Tuple(0, Odd(n))))),
Variables(n),
Assumptions(Element(n, ZZGreaterEqual(0))))

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