Generalized Hypergeometric Functions & Meijer G -Function - 16.16 Transformations of Variables

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
16.16.E5	${\displaystyle{\displaystyle{F_{3}}\left(\alpha,\gamma-\alpha;\beta,\gamma-\beta;\gamma;x,y\right)=(1-y)^{\alpha+\beta-\gamma}{{}_{2}F_{1}}\left({\alpha,\beta\atop\gamma};x+y-xy\right)}}$ \AppellF{3}@{\alpha}{\gamma-\alpha}{\beta}{\gamma-\beta}{\gamma}{x}{y} = (1-y)^{\alpha+\beta-\gamma}\genhyperF{2}{1}@@{\alpha,\beta}{\gamma}{x+y-xy}		Error	AppellF[3, , \[Alpha], \[Gamma]- \[Alpha], \[Beta], \[Gamma]- \[Beta]]*\[Gamma]*x*y == (1 - y)^(\[Alpha]+ \[Beta]- \[Gamma])* HypergeometricPFQ[{\[Alpha], \[Beta]}, {\[Gamma]}, x + y - x*y]	Missing Macro Error	Failure	-	Failed [300 / 300] Result: Plus[Complex[0.33907796278424684, 2.1694931088262193], Times[Complex[-1.948557158514987, -1.1249999999999998], AppellF[3.0, Null, 1.5, Complex[-0.6339745962155613, 0.49999999999999994], 1.5, Complex[-0.6339745962155613, 0.49999999999999994]]]] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Plus[Complex[3.1592684418872854, 2.774129956365469], Times[Complex[1.1249999999999996, -1.948557158514987], AppellF[3.0, Null, 1.5, Complex[-1.9999999999999998, 0.8660254037844387], 1.5, Complex[-1.9999999999999998, 0.8660254037844387]]]] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
16.16.E6	${\displaystyle{\displaystyle{F_{4}}\left(\alpha,\beta;\gamma,\alpha+\beta-\gamma+1;x(1-y),y(1-x)\right)={{}_{2}F_{1}}\left({\alpha,\beta\atop\gamma};x\right){{}_{2}F_{1}}\left({\alpha,\beta\atop\alpha+\beta-\gamma+1};y\right)}}$ \AppellF{4}@{\alpha}{\beta}{\gamma}{\alpha+\beta-\gamma+1}{x(1-y)}{y(1-x)} = \genhyperF{2}{1}@@{\alpha,\beta}{\gamma}{x}\genhyperF{2}{1}@@{\alpha,\beta}{\alpha+\beta-\gamma+1}{y}		Error	AppellF[4, , \[Alpha], \[Beta], \[Gamma], \[Alpha]+ \[Beta]- \[Gamma]+ 1]*x*(1 - y)*y*(1 - x) == HypergeometricPFQ[{\[Alpha], \[Beta]}, {\[Gamma]}, x]*HypergeometricPFQ[{\[Alpha], \[Beta]}, {\[Alpha]+ \[Beta]- \[Gamma]+ 1}, y]	Missing Macro Error	Failure	-	Skip - No test values generated