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Fungrim entry: 1c3766

sinc⁡(n)(0)={(−1)⌊n/2⌋1n+1,n even0,n odd{\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∈Z≥0n \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
ComplexDerivativeddz f ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative
Sincsinc⁡(z)\operatorname{sinc}(z) Sinc function
Powab{a}^{b} Power
ZZGreaterEqualZ≥n\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))))

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2021-03-15 19:12:00.328586 UTC