I am plotting the following function $\frac{\sqrt{t \text{$\omega_c $}}-\sqrt{\pi } e^{\frac{1}{t \text{$\omega_c $}}} \text{erfc}\left(\frac{1}{\sqrt{t \text{$\omega_c$}}}\right)}{(t \text{$\omega_c$})^{3/2}}$ for $\omega_c=1$

 (Sqrt[t*\[Omega]c] - E^(1/(t*\[Omega]c))*Sqrt[Pi]*Erfc[1/Sqrt[t*\[Omega]c]])/(t*\[Omega]c)^(3/2)

and I am obtaining

enter image description here

where we clearly see that the function diverges as $t \rightarrow 0$. What is interesting is that if I perform the limit through Mathematica for $t\rightarrow 0$ I obtain

enter image description here

which clearly disagrees with the graph. It is important to note that for $t\approx 10^{-3}$ the graph tends to the same correct limit, indicated by the blue line. Is there any way to increase the precision of the plot?

  • 5
    $\begingroup$ Plot[..., WorkingPrecision -> 20] $\endgroup$ Sep 27, 2021 at 22:18