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Fungrim entry: 6c28fa

sinc ⁣()=limxsinc ⁣(ai+x)=0\operatorname{sinc}\!\left(-\infty\right) = \lim_{x \to -\infty} \operatorname{sinc}\!\left(a i + x\right) = 0
Assumptions:aCa \in \mathbb{C}
TeX:
\operatorname{sinc}\!\left(-\infty\right) = \lim_{x \to -\infty} \operatorname{sinc}\!\left(a i + x\right) = 0

a \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Sincsinc(z)\operatorname{sinc}(z) Sinc function
Infinity\infty Positive infinity
RealLimitlimxaf(x)\lim_{x \to a} f(x) Limiting value, real variable
ConstIii Imaginary unit
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("6c28fa"),
    Formula(Equal(Sinc(Neg(Infinity)), RealLimit(Sinc(Add(Mul(a, ConstI), x)), For(x, Neg(Infinity))), 0)),
    Variables(a),
    Assumptions(Element(a, CC)))

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

2020-01-31 18:09:28.494564 UTC