Gold 33

Scorer's function

Gold ID

33

Link

https://sigir21.wmflabs.org/wiki/Scorer's_function#math.83.3

Formula

$\mathrm{G}\mathrm{i}(x)=\frac{1}{\pi }\underset{0}{\overset{\mathrm{\infty }}{\int }}\sin (\frac{t^3}{3}+xt)dt$

TeX Source

\mathrm{Gi}(x) = \frac{1}{\pi} \int_0^\infty \sin\left(\frac{t^3}{3} + xt\right)\, dt

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations

Semantic LaTeX

Translation

\ScorerGi@{x} = \frac{1}{\cpi} \int_0^\infty \sin(\frac{t^3}{3} + xt) \diff{t}

Expected (Gold Entry)

\ScorerGi@{x} = \frac{1}{\cpi} \int_0^\infty \sin(\frac{t^3}{3} + xt) \diff{t}

Mathematica

Translation

ScorerGi[x] == Divide[1,Pi]*Integrate[Sin[Divide[(t)^(3),3]+ x*t], {t, 0, Infinity}, GenerateConditions->None]

Expected (Gold Entry)

ScorerGi[x] == Divide[1,Pi]*Integrate[Sin[Divide[(t)^(3),3]+ x*t], {t, 0, Infinity}]

Maple

Translation

AiryBi(x)*(int(AiryAi(t), t = (x) .. infinity))+AiryAi(x)*(int(AiryBi(t), t = 0 .. (x))) = (1)/(Pi)*int(sin(((t)^(3))/(3)+ x*t), t = 0..infinity)

Expected (Gold Entry)

AiryBi(x)*(int(AiryAi(t), t = (x) .. infinity))+AiryAi(x)*(int(AiryBi(t), t = 0 .. (x))) = (1)/(Pi)*int(sin(((t)^(3))/(3)+ x*t), t = 0..infinity)