[pstricks] plot erfc and Bessel function with pstricks

Herbert Voss Herbert.Voss at FU-Berlin.DE
Fri Oct 21 21:51:23 CEST 2011

> http://en.wikipedia.org/wiki/Bessel_function#Modified_Bessel_functions_:_I.CE.B1.2C_K.CE.B1
>
>
> i hope I explained the topic better this time.

Hope, this helps:

\documentclass{article}
\usepackage{pst-func}

\makeatletter
\define at key[psset]{pst-func}{nu}[1]{\def\psk at nu{#1 }}
\psset{nu=0}
%
\def\psModBessel{\@ifnextchar[{\psModBessel at i}{\psModBessel at i[]}}
\def\psModBessel at i[#1]#2#3{{%%%  #2 = n
\pst at killglue
\psset{#1}%
\psplot{#2}{#3}[ /nu \psk at nu def /epsilon 1e-20 def
/Fact { 1 exch 2 exch 1 exch { mul } for } def
/Gamma { 1 sub Fact } def ]{%
/Sum 0 def
/Iter 0 def
{/Sum_Iter
x dup mul 4 div Iter exp        % nominator
nu Iter add 1 add Gamma Iter Fact mul  % denominator
Div def
Sum_Iter abs epsilon lt { exit } if
/Sum Sum Sum_Iter add def
/Iter Iter 1 add  def Iter ==
} loop
x 0.5 mul nu exp Sum mul
}%
}\ignorespaces}

\makeatother
\begin{document}
$I_\nu(x)=\left(\frac12 x\right)^\nu \sum\limits_{k=0}^{\infty} \frac{{\left(\frac14 x^2\right)}^k}{k!\Gamma(\nu+k+1)}$

\begin{pspicture}(5,5)
\psaxes(5,5)
\multido{\iA=0+1}{5}{\psModBessel[yMaxValue=5,nu=\iA]{0}{5}}
\end{pspicture}

\end{document}

Herbert

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