Gold 29

Sinc function

Gold ID

29

Link

https://sigir21.wmflabs.org/wiki/Sinc_function#math.79.11

Formula

$\underset{-\mathrm{\infty }}{\overset{\mathrm{\infty }}{\int }}\mathrm{sinc}(t)e^{-i2\pi ft}dt=\mathrm{rect}(f)$

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

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)