I need to plot a function that uses the built-in HyperGeometric 2F1 function. First I want to print out the value of the function in a couple of points. But the printed value just shows the 2F1 function with arguments, not the actual value of the function.
Here is my Notebook entry:
Clear[z1, zEQ, dFS1, dFS2, z]
z1 = 0.4*10^6
zEQ = 3400
dFS1[z_] = (15.6/Sqrt[z])*HyperGeometric2F1[1/2, 1/6, 7/6, -2.33/z^3]*
UnitStep[z - z1]
Evaluate[dFS1[10^9]]
Evaluate[dFS1[0.4*10^6]]
dFS2[z_] =
15.6*{(1/Sqrt[z1])*
HyperGeometric2F1[1/2, 1/6,
7/6, -2.33/z1^3] + ((z + 1)/z1^(3/2))*
HyperGeometric2F1[1/2, -1/6, 5/6, -2.33/z1^3] - (Sqrt[z + 1]/z1)*
HyperGeometric2F1[1/2, -1/6, 5/6, -2.33/(z + 1)^3]}*
UnitStep[z1 - z]
Evaluate[dFS2[0.4*10^6]]
Evaluate[dFS2[0]]
LogLogPlot[{dFS1[z], dFS2[z]}, {z, 10^9,
0}, {ScalingFunctions -> "Reverse", PlotRange -> Full}]
Here are the results of the first two Evaluates:
0.000493315 HyperGeometric2F1(1/2,1/6,7/6,-2.33*10^-27) (* for dFS1[10^9] *)
0.0246658 HyperGeometric2F1(1/2,1/6,7/6,-3.64063*10^-17) (* for dFS1[0.4*10^6] *)
The reason I want to get the numerical values is that the LogLogPlot does not show any data, it just shows an empty plot (and starts at z = 10^6?). I would also like any advice on how to get the Plot to show my function.
I tried just plain dFS[z1] first, then tried Simplify[dFS[z1]], ExpandAll[dFS[z1]], Evaluate[dFS[z1]], and last Evaluate[dFS[0.4*10^6]]. I also tried to wrap the two function definitions with Simplify[,z>=0], thinking that maybe Mathematica thought z is complex.
They all returned the same expression, already shown above.