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authorNorbert Preining <norbert@preining.info>2020-06-07 03:03:23 +0000
committerNorbert Preining <norbert@preining.info>2020-06-07 03:03:23 +0000
commit666248863665f4318b13e1c1b7a2b94ef90a8b9a (patch)
tree9e682f3dd1e75d918244c2e0d615e58850a0e1e4 /graphics/pstricks/contrib/pst-func/doc/pst-func-doc.tex
parent527cbc8280407d055d185ad11f79b81b032eec7e (diff)
CTAN sync 202006070303
Diffstat (limited to 'graphics/pstricks/contrib/pst-func/doc/pst-func-doc.tex')
-rw-r--r--graphics/pstricks/contrib/pst-func/doc/pst-func-doc.tex69
1 files changed, 66 insertions, 3 deletions
diff --git a/graphics/pstricks/contrib/pst-func/doc/pst-func-doc.tex b/graphics/pstricks/contrib/pst-func/doc/pst-func-doc.tex
index bf8628902f..cf3819048b 100644
--- a/graphics/pstricks/contrib/pst-func/doc/pst-func-doc.tex
+++ b/graphics/pstricks/contrib/pst-func/doc/pst-func-doc.tex
@@ -1,4 +1,4 @@
-%% $Id: pst-func-doc.tex 861 2018-12-13 20:40:06Z herbert $
+%% $Id: pst-func-doc.tex 1184 2020-06-06 18:36:57Z herbert $
\documentclass[fontsize=11pt,english,BCOR=10mm,DIV=12,bibliography=totoc,parskip=false,
headings=small, headinclude=false,footinclude=false,oneside]{pst-doc}
\usepackage{pst-func}
@@ -607,6 +607,68 @@ which plots the envelope curve instead of the Bernstein polynomial.
\clearpage
+
+
+\subsection{Laguerre Polynomial}
+It is defined as
+\[
+L_n(x)=\sum_{k=0}^n\frac{(-1)^k}{k!}\binom{n}{k}x^k
+\]
+
+\begin{LTXexample}
+\psset{xunit=1.5}
+\begin{pspicture}(-1,-4)(6,6)
+\psaxes{->}(0,0)(-1,-4)(5,6)
+\psset{yMaxValue=5,plotpoints=100,linewidth=1pt}
+\psLaguerre[n=0,linecolor=red](-1,5)\uput[0](5,1){$L_0$}
+\psLaguerre[n=1,linecolor=green](-1,5)\uput[0](4,-2.5){$L_1$}
+\psLaguerre[n=2,linecolor=blue](-1,5)\uput[0](4.5,2){$L_2$}
+\psLaguerre[n=3,linecolor=yellow](-1,5)\uput[0](5,2.5){$L_3$}
+\psLaguerre[n=4,linecolor=brown](-1,5)\uput[0](5,-1){$L_4$}
+\end{pspicture}
+\end{LTXexample}
+
+
+\psset{unit=1cm}
+
+\clearpage
+
+
+\subsection{Legendre Polynomial}
+It is defined as an orthogonal system
+\[
+\int\limits_{-1}^{+1}P_m(x)(P_n(x)\mathrm dx=0, \text{ with } n\ne m
+\]
+
+For the computatíon we use a recursive definition:
+
+\begin{align*}
+P_0(x) &= 1\\
+P_{1}(x) &= x\\
+n\cdot P_{n}(x) &= (2n-1)x\cdot P_{n-1}(x)-(n-1)P_{n-2}(x)
+\end{align*}
+
+
+\begin{LTXexample}
+\psset{xunit=3,yunit=2}
+\begin{pspicture}[showgrid](-2,-2)(2,2)
+\psaxes[labels=none]{->}(0,0)(-2,-2)(2,2)
+\psset{yMaxValue=1.9,yMinValue=-2,plotpoints=200,linewidth=1.5pt}
+\psLegendre[n=0,linecolor=red](-2,2)\uput[0](2,1){\textcolor{red}{$L_0$}}
+\psLegendre[n=1,linecolor=green](-2,2)\uput[0](2,2){\textcolor{green}{$L_1$}}
+\psLegendre[n=2,linecolor=blue](-2,2)\uput[0](1.3,1.8){\textcolor{blue}{$L_2$}}
+\psLegendre[n=3,linecolor=yellow](-2,2)\uput*[0](-1,-1.8){\textcolor{yellow}{$L_3$}}
+\psLegendre[n=4,linecolor=brown](-2,2)\uput*[0](-1,2){\textcolor{brown}{$L_4$}}
+\end{pspicture}
+\end{LTXexample}
+
+
+\psset{unit=1cm}
+
+
+
+
+\clearpage
\section{Calculating the zeros of a function or the the intermediate point of two function}
\begin{BDef}
@@ -1136,8 +1198,6 @@ way, at the cost of some reduction in graphics resolution.
\end{LTXexample}
\clearpage
-
-\clearpage
\section{Modfied Bessel function of first order}
The modified Bessel function of first order is defined as
%
@@ -1166,6 +1226,9 @@ is preset to 0, it shows $I_0$.
\end{LTXexample}
\clearpage
+
+
+
\section{\Lcs{psSi}, \Lcs{pssi} and \Lcs{psCi}}
The integral sin and cosin are defined as
%