diff options
Diffstat (limited to 'Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex')
-rw-r--r-- | Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex | 69 |
1 files changed, 66 insertions, 3 deletions
diff --git a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex index bf8628902f5..cf3819048b0 100644 --- a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex +++ b/Master/texmf-dist/doc/generic/pst-func/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 computatÃon 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 % |