Airy and Related Functions - 9.13 Generalized Airy Functions

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
9.13#Ex7	${\displaystyle{\displaystyle m=n+2}}$ m = n+2		m = n + 2	m == n + 2	Skipped - no semantic math	Skipped - no semantic math	-	-
9.13#Ex8	${\displaystyle{\displaystyle t=(\tfrac{1}{2}m)^{-2/m}z}}$ t = (\tfrac{1}{2}m)^{-2/m}z		t = ((1)/(2)*m)^(- 2/m)* z	t == (Divide[1,2]*m)^(- 2/m)* z	Skipped - no semantic math	Skipped - no semantic math	-	-
9.13.E20	${\displaystyle{\displaystyle U_{1}(x,\alpha)=\frac{1}{(\alpha+2)^{1/(\alpha+2)}}\*\Gamma\left(\frac{\alpha+1}{\alpha+2}\right)x^{1/2}J_{-1/(\alpha+2)}\left(\frac{2}{\alpha+2}x^{(\alpha+2)/2}\right)}}$ U_{1}(x,\alpha) = \frac{1}{(\alpha+2)^{1/(\alpha+2)}}\*\EulerGamma@{\frac{\alpha+1}{\alpha+2}}x^{1/2}\BesselJ{-1/(\alpha+2)}@{\frac{2}{\alpha+2}x^{(\alpha+2)/2}}		U[1](x , alpha) = (1)/((alpha + 2)^(1/(alpha + 2)))* GAMMA((alpha + 1)/(alpha + 2))*(x)^(1/2)* BesselJ(- 1/(alpha + 2), (2)/(alpha + 2)*(x)^((alpha + 2)/2))	Subscript[U, 1][x , \[Alpha]] == Divide[1,(\[Alpha]+ 2)^(1/(\[Alpha]+ 2))]* Gamma[Divide[\[Alpha]+ 1,\[Alpha]+ 2]]*(x)^(1/2)* BesselJ[- 1/(\[Alpha]+ 2), Divide[2,\[Alpha]+ 2]*(x)^((\[Alpha]+ 2)/2)]	Failure	Failure	Error	Error
9.13.E21	${\displaystyle{\displaystyle U_{2}(x,\alpha)=(\alpha+2)^{1/(\alpha+2)}\*\Gamma\left(\frac{\alpha+3}{\alpha+2}\right)x^{1/2}J_{1/(\alpha+2)}\left(\frac{2}{\alpha+2}x^{(\alpha+2)/2}\right)}}$ U_{2}(x,\alpha) = (\alpha+2)^{1/(\alpha+2)}\*\EulerGamma@{\frac{\alpha+3}{\alpha+2}}x^{1/2}\BesselJ{1/(\alpha+2)}@{\frac{2}{\alpha+2}x^{(\alpha+2)/2}}		U[2](x , alpha) = (alpha + 2)^(1/(alpha + 2))* GAMMA((alpha + 3)/(alpha + 2))*(x)^(1/2)* BesselJ(1/(alpha + 2), (2)/(alpha + 2)*(x)^((alpha + 2)/2))	Subscript[U, 2][x , \[Alpha]] == (\[Alpha]+ 2)^(1/(\[Alpha]+ 2))* Gamma[Divide[\[Alpha]+ 3,\[Alpha]+ 2]]*(x)^(1/2)* BesselJ[1/(\[Alpha]+ 2), Divide[2,\[Alpha]+ 2]*(x)^((\[Alpha]+ 2)/2)]	Failure	Failure	Error	Error
9.13#Ex9	${\displaystyle{\displaystyle\alpha=m-2}}$ \alpha = m-2		alpha = m - 2	\[Alpha] == m - 2	Skipped - no semantic math	Skipped - no semantic math	-	-
9.13#Ex10	${\displaystyle{\displaystyle x=(m/2)^{2/m}t}}$ x = (m/2)^{2/m}t		x = (m/2)^(2/m)* t	x == (m/2)^(2/m)* t	Skipped - no semantic math	Skipped - no semantic math	-	-
9.13.E23	${\displaystyle{\displaystyle U_{1}(x,\alpha)=\frac{\pi^{1/2}}{2^{(m+2)/(2m)}\Gamma\left(1/m\right)}\left(W_{m}(t)+W_{m}(-t)\right)}}$ U_{1}(x,\alpha) = \frac{\pi^{1/2}}{2^{(m+2)/(2m)}\EulerGamma@{1/m}}\left(W_{m}(t)+W_{m}(-t)\right)	${\displaystyle{\displaystyle\Re(1/m)>0}}$	U[1](x , alpha) = ((Pi)^(1/2))/((2)^((m + 2)/(2*m))* GAMMA(1/m))*(W[m](t)+ W[m](- t))	Subscript[U, 1][x , \[Alpha]] == Divide[(Pi)^(1/2),(2)^((m + 2)/(2*m))* Gamma[1/m]]*(Subscript[W, m][t]+ Subscript[W, m][- t])	Failure	Failure	Error	Error
9.13.E24	${\displaystyle{\displaystyle U_{2}(x,\alpha)=\frac{\pi^{1/2}m^{2/m}}{2^{(m+2)/(2m)}\Gamma\left(-1/m\right)}\left(W_{m}(t){-}W_{m}(-t)\right)}}$ U_{2}(x,\alpha) = \frac{\pi^{1/2}m^{2/m}}{2^{(m+2)/(2m)}\EulerGamma@{-1/m}}\left(W_{m}(t){-}W_{m}(-t)\right)	${\displaystyle{\displaystyle\Re(-1/m)>0}}$	U[2](x , alpha) = ((Pi)^(1/2)* (m)^(2/m))/((2)^((m + 2)/(2*m))* GAMMA(- 1/m))*(W[m](t)- W[m](- t))	Subscript[U, 2][x , \[Alpha]] == Divide[(Pi)^(1/2)* (m)^(2/m),(2)^((m + 2)/(2*m))* Gamma[- 1/m]]*(Subscript[W, m][t]- Subscript[W, m][- t])	Failure	Failure	Error	Error