Gold 29

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Sinc function

Gold ID
29
Link
https://sigir21.wmflabs.org/wiki/Sinc_function#math.79.11
Formula
sinc(t)ei2πftdt=rect(f)
TeX Source
\int_{-\infty}^\infty \operatorname{sinc}(t) \, e^{-i 2 \pi f t}\,dt = \operatorname{rect}(f)
Translation Results
Semantic LaTeX Mathematica Translation Maple Translations
Yes Yes Yes

Semantic LaTeX

Translation
\int_{-\infty}^\infty \operatorname{sinc}(t) \expe^{- \iunit 2 \cpi f t} \diff{t} = \operatorname{rect}(f)
Expected (Gold Entry)
\int_{-\infty}^\infty \operatorname{sinc}(t) \expe^{- \iunit 2 \cpi f t} \diff{t} = \operatorname{rect}(f)


Mathematica

Translation
Integrate[sinc[t]* Exp[- I*2*Pi*f*t], {t, - Infinity, Infinity}, GenerateConditions->None] == rect[f]
Expected (Gold Entry)
Integrate[sinc[(t)]*Exp[- I*2*Pi*f*t], {t, - Infinity, Infinity}] == rect[f]


Maple

Translation
int(sinc(t)* exp(- I*2*Pi*f*t), t = - infinity..infinity) = rect(f)
Expected (Gold Entry)
int(sinc((t))*exp(- I*2*Pi*f*t), t = - infinity..infinity) = rect(f)