[pstricks] a function defined by an infinite serie

[Christoph Bersch]

Hi,

Am 15.02.2013 13:00, schrieb Cyrille Piatecki:
>
> I wonder how to plot under pstricks the following function
>
> \varepsilon(t) = \sum_{n=0}^\infty \frac{\rho^n \cdot t^{n \cdot
> \alpha}}{\Gamma(n\cdot\alpha +1)}\cdot \epsilon_0
>
> for  whichever \rho --- positif or negatif --- and 0<  \alpha<= 1

try this:

\documentclass{article}
\usepackage{pst-plot, pst-math}
\begin{document}
% #1 is \rho, #2 is \alpha, #3 is summation limit
\def\epsilonfunc#1#2#3{%
   0 % start value for summation
   0 1 #3 {
     dup #1 exch exp exch #2 mul dup
     x exch exp 3 -1 roll mul exch 1 add GAMMA div add
   } for
}%
\begin{pspicture}[showgrid](10,10)
\psplot[plotpoints=30, showpoints]{0}{10}{\epsilonfunc{0.2}{0.5}{30}}
\end{pspicture}
\end{document}

This is with a fixed summation, I don't know the function behavior, so 
what truncation criterium might be used.

Christoph