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Fungrim entry: 50f72f

sinc(z)=z30F1 ⁣(52,z24)\operatorname{sinc}'(z) = -\frac{z}{3} \,{}_0F_1\!\left(\frac{5}{2}, -\frac{{z}^{2}}{4}\right)
Assumptions:zCz \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
Derivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Derivative
Sincsinc(z)\operatorname{sinc}(z) Sinc function
Hypergeometric0F10F1 ⁣(a,z)\,{}_0F_1\!\left(a, z\right) Confluent hypergeometric limit function
Powab{a}^{b} Power
CCC\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)))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-08-27 09:56:25.682319 UTC