I am working with a function in Mathematica and I am getting some inconsistencies when I plot it. As I really need to understand were this comes from I would appreciate any help.
I am working with a function of the following form:
f2b[b_] = Exp[-1000 - 2 Sqrt[1000*b] - b]*(Erfi[Sqrt[1000]] - Erfi[Sqrt[1000] + Sqrt[b]])
From my understanding this function should go to zero for very small b because both parts, the Exp function as well as the difference between the imaginary error functions, should vanish.
Mathematica calculates:
f2b[E^-30] // N = -3.4517046881*10^-7 as expected.
BUT if I plot this function:
Plot[{f2b[E^b], 0}, {b, -50, 0}, PlotStyle -> {{Blue, Thick}, {Red, Thick}}]
Mathematica shows me a plot which is approaching a value of about -0.0175 for small b and has therefore an absolute value much larger the the value at E^-30 calculated above.
If I tabulate, interpolate and plot the function:
t = Table[{b, f2b[E^b] // N}, {b, -50, 0}]; f = Interpolation[t]; Plot[{f[b], 0}, {b, -50, 0}, PlotStyle -> {{Blue, Thick}, {Red, Thick}}]
The plot is looking much different and is approaching zero as expected.
I am wondering whether this has to do something with overflow problems in graphics but I am not sure.
Thanks in advance.
Silky
