Gold 18

Fresnel integral

Gold ID: 18
Link: https://sigir21.wmflabs.org/wiki/Fresnel_integral#math.68.51
Formula: $\begin{aligned} \int x^{m} e^{i x^{n}} d x & = \frac{x^{m + 1}}{m + 1}_{1} F_{1} (\begin{array}{c} \frac{m + 1}{n} \\ 1 + \frac{m + 1}{n} \end{array} ∣ i x^{n}) \\ [6 p x] & = \frac{1}{n} i^{\frac{m + 1}{n}} γ (\frac{m + 1}{n}, - i x^{n}), \end{aligned}$
TeX Source: \begin{align}\int x^m e^{ix^n}\,dx & =\frac{x^{m+1}}{m+1}\,_1F_1\left(\begin{array}{c} \frac{m+1}{n}\\1+\frac{m+1}{n}\end{array}\mid ix^n\right) \\[6px]& =\frac{1}{n} i^\frac{m+1}{n}\gamma\left(\frac{m+1}{n},-ix^n\right),\end{align}

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations

Translation: \begin{align}\int x^m \expe^{\iunit x^n} \diff{x} &= \frac{x^{m+1}}{m+1}_1 F_1(\begin{array}{c} \frac{m+1}{n}\\1+\frac{m+1}{n}\end{array} \mid \iunit x^n) \\ &= \frac{1}{n} \iunit^\frac{m+1}{n} \incgamma@{\frac{m+1}{n}}{- \iunit x^n} ,\end{align}
Expected (Gold Entry): \begin{align}\int x^m \exp(\iunit x^n) \diff{x} &= \frac{x^{m+1}}{m+1}\genhyperF{1}{1}@{\frac{m+1}{n}}{1+\frac{m+1}{n}}{\iunit x^n}\\ &=\frac{1}{n} \iunit^{(m+1)/n} \incgamma@{\frac{m+1}{n}}{-\iunit x^n}\end{align}

Translation
Expected (Gold Entry): Integrate[(x)^(m)* Exp[I*(x)^(n)], x] == Divide[(x)^(m + 1),m + 1]*HypergeometricPFQ[{Divide[m + 1,n]}, {1 +Divide[m + 1,n]}, I*(x)^(n)] == Divide[1,n]*(I)^((m + 1)/n)* Gamma[Divide[m + 1,n], 0, - I*(x)^(n)]

Translation
Expected (Gold Entry): int((x)^(m)* exp(I*(x)^(n)), x) = ((x)^(m + 1))/(m + 1)*hypergeom([(m + 1)/(n)], [1 +(m + 1)/(n)], I*(x)^(n)) = (1)/(n)*(I)^((m + 1)/n)* GAMMA((m + 1)/(n))-GAMMA((m + 1)/(n), - I*(x)^(n))