Functions of Matrix Argument - 36.2 Catastrophes and Canonical Integrals

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
36.2#Ex2	${\displaystyle{\displaystyle\mathrm{F}_{+}(\mathbf{x})=\int_{0}^{\infty}\cos\left(ry\exp\left(+i\dfrac{\pi}{6}\right)\right)\exp\left(2ir^{2}z\exp\left(+i\dfrac{\pi}{3}\right)\right)\mathrm{Ai}\left(3^{2/3}r^{2}+3^{-1/3}\exp\left(-i\dfrac{\pi}{3}\right)\left(\tfrac{1}{3}z^{2}-x\right)\right)\mathrm{d}r}}$ \mathrm{F}_{+}(\mathbf{x}) = \int_{0}^{\infty}\cos@{ry\exp@{+ i\dfrac{\pi}{6}}}\exp@{2ir^{2}z\exp@{+ i\dfrac{\pi}{3}}}\AiryAi@{3^{2/3}r^{2}+3^{-1/3}\exp@{- i\dfrac{\pi}{3}}\left(\tfrac{1}{3}z^{2}-x\right)}\diff{r}		F[+](x) = int(cos(r*y*exp(+ I*(Pi)/(6)))*exp(2*I*(r)^(2)*(x + y*I)*exp(+ I*(Pi)/(3)))*AiryAi((3)^(2/3)* (r)^(2)+ (3)^(- 1/3)* exp(- I*(Pi)/(3))*((1)/(3)*(x + y*I)^(2)- x)), r = 0..infinity)	Subscript[F, +][x] == Integrate[Cos[r*y*Exp[+ I*Divide[Pi,6]]]*Exp[2*I*(r)^(2)*(x + y*I)*Exp[+ I*Divide[Pi,3]]]*AiryAi[(3)^(2/3)* (r)^(2)+ (3)^(- 1/3)* Exp[- I*Divide[Pi,3]]*(Divide[1,3]*(x + y*I)^(2)- x)], {r, 0, Infinity}, GenerateConditions->None]	Error	Failure	-	Error
36.2#Ex2	${\displaystyle{\displaystyle\mathrm{F}_{-}(\mathbf{x})=\int_{0}^{\infty}\cos\left(ry\exp\left(-i\dfrac{\pi}{6}\right)\right)\exp\left(2ir^{2}z\exp\left(-i\dfrac{\pi}{3}\right)\right)\mathrm{Ai}\left(3^{2/3}r^{2}+3^{-1/3}\exp\left(+i\dfrac{\pi}{3}\right)\left(\tfrac{1}{3}z^{2}-x\right)\right)\mathrm{d}r}}$ \mathrm{F}_{-}(\mathbf{x}) = \int_{0}^{\infty}\cos@{ry\exp@{- i\dfrac{\pi}{6}}}\exp@{2ir^{2}z\exp@{- i\dfrac{\pi}{3}}}\AiryAi@{3^{2/3}r^{2}+3^{-1/3}\exp@{+ i\dfrac{\pi}{3}}\left(\tfrac{1}{3}z^{2}-x\right)}\diff{r}		F[-](x) = int(cos(r*y*exp(- I*(Pi)/(6)))*exp(2*I*(r)^(2)*(x + y*I)*exp(- I*(Pi)/(3)))*AiryAi((3)^(2/3)* (r)^(2)+ (3)^(- 1/3)* exp(+ I*(Pi)/(3))*((1)/(3)*(x + y*I)^(2)- x)), r = 0..infinity)	Subscript[F, -][x] == Integrate[Cos[r*y*Exp[- I*Divide[Pi,6]]]*Exp[2*I*(r)^(2)*(x + y*I)*Exp[- I*Divide[Pi,3]]]*AiryAi[(3)^(2/3)* (r)^(2)+ (3)^(- 1/3)* Exp[+ I*Divide[Pi,3]]*(Divide[1,3]*(x + y*I)^(2)- x)], {r, 0, Infinity}, GenerateConditions->None]	Error	Failure	-	Error
36.2.E14	${\displaystyle{\displaystyle P(x_{2},x_{1})=\int_{-\infty}^{\infty}\exp\left(\mathrm{i}(t^{4}+x_{2}t^{2}+x_{1}t)\right)\mathrm{d}t}}$ P(x_{2},x_{1}) = \int_{-\infty}^{\infty}\exp@{\iunit(t^{4}+x_{2}t^{2}+x_{1}t)}\diff{t}		P(x[2], x[1]) = int(exp(I*((t)^(4)+ x[2]*(t)^(2)+ x[1]*t)), t = - infinity..infinity)	P[Subscript[x, 2], Subscript[x, 1]] == Integrate[Exp[I*((t)^(4)+ Subscript[x, 2]*(t)^(2)+ Subscript[x, 1]*t)], {t, - Infinity, Infinity}, GenerateConditions->None]	Failure	Failure	Skipped - Because timed out	Error
36.2#Ex10	${\displaystyle{\displaystyle\tfrac{1}{3}\sqrt{\pi}\Gamma\left(\tfrac{1}{6}\right)=3.28868}}$ \tfrac{1}{3}\sqrt{\pi}\EulerGamma@{\tfrac{1}{6}} = 3.28868		(1)/(3)*sqrt(Pi)*GAMMA((1)/(6)) = 3.28868	Divide[1,3]*Sqrt[Pi]*Gamma[Divide[1,6]] == 3.28868	Failure	Failure	Successful [Tested: 0]	Successful [Tested: 1]
36.2#Ex11	${\displaystyle{\displaystyle\tfrac{1}{3}{\Gamma^{2}}\left(\tfrac{1}{3}\right)=2.39224}}$ \tfrac{1}{3}\EulerGamma^{2}@{\tfrac{1}{3}} = 2.39224		(1)/(3)*(GAMMA((1)/(3)))^(2) = 2.39224	Divide[1,3]*(Gamma[Divide[1,3]])^(2) == 2.39224	Failure	Failure	Successful [Tested: 0]	Successful [Tested: 1]