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Diffstat (limited to 'Master/texmf-dist')
-rw-r--r-- | Master/texmf-dist/doc/generic/pst-func/Changes | 2 | ||||
-rw-r--r-- | Master/texmf-dist/doc/generic/pst-func/README.md | 4 | ||||
-rw-r--r-- | Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf | bin | 3956145 -> 3889616 bytes | |||
-rw-r--r-- | Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex | 69 | ||||
-rw-r--r-- | Master/texmf-dist/tex/generic/pst-func/pst-func.tex | 48 |
5 files changed, 117 insertions, 6 deletions
diff --git a/Master/texmf-dist/doc/generic/pst-func/Changes b/Master/texmf-dist/doc/generic/pst-func/Changes index cd9eec4c30f..32534e1f7fd 100644 --- a/Master/texmf-dist/doc/generic/pst-func/Changes +++ b/Master/texmf-dist/doc/generic/pst-func/Changes @@ -1,4 +1,6 @@ ..... pst-func.tex +0.95 2020-06-06 - another two more polynomial functions +0.94 2020-01-01 - small fixes 0.93 2019-05-17 - fix for missing end in a local dictionary (\psBinomialX) 0.92 2018-12-13 - allow algebraic mode for \pscumIntegral 0.91 2018-11-15 - new algorithm for sin/cos integral to prevent problems diff --git a/Master/texmf-dist/doc/generic/pst-func/README.md b/Master/texmf-dist/doc/generic/pst-func/README.md index 3297389d3e7..d7afcc5c615 100644 --- a/Master/texmf-dist/doc/generic/pst-func/README.md +++ b/Master/texmf-dist/doc/generic/pst-func/README.md @@ -6,6 +6,8 @@ - psBernstein (with envelope option) - psFourier - psBessel +- psLagrange +- psLegendre - psSi and pssi (integral sin) - psCi and \psci (integral cosin) - psIntegral @@ -45,3 +47,5 @@ with pdftex, use the sequence latex->dvips->ps2pdf or pdflatex with package auto-pst-pdf or xelatex. %% $Id: README 897 2014-03-21 08:06:41Z herbert $ + +Bugs: hvoss@tug.org
\ No newline at end of file diff --git a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf Binary files differindex e3f65b7c0cd..740e2568d6b 100644 --- a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf +++ b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf 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 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 % diff --git a/Master/texmf-dist/tex/generic/pst-func/pst-func.tex b/Master/texmf-dist/tex/generic/pst-func/pst-func.tex index 0bef36090b6..c581b1e49f1 100644 --- a/Master/texmf-dist/tex/generic/pst-func/pst-func.tex +++ b/Master/texmf-dist/tex/generic/pst-func/pst-func.tex @@ -1,4 +1,4 @@ -%% $Id: pst-func.tex 861 2018-12-13 20:40:06Z herbert $ +%% $Id: pst-func.tex 1184 2020-06-06 18:36:57Z herbert $ %% %% This is file `pst-func.tex', %% @@ -31,8 +31,8 @@ % interface to the `xkeyval' package \pst@addfams{pst-func} % -\def\fileversion{0.93} -\def\filedate{2019/05/17} +\def\fileversion{0.95} +\def\filedate{2020/06/06} \message{`PST-func' v\fileversion, \filedate\space (hv)} % \pstheader{pst-func.pro} @@ -268,6 +268,48 @@ }% }\ignorespaces} % +\define@key[psset]{pst-func}{n}[1]{\def\psk@func@n{#1 }} +\psset[pst-func]{n=0} +\def\psLaguerre{\@ifnextchar[{\psLaguerre@i}{\psLaguerre@i[]}}%% hv 20200111 +\def\psLaguerre@i[#1](#2,#3){{%%% n + \pst@killglue% + \psplot[#1]{#2}{#3}{% + /L_n 1 def + 0 1 \psk@func@n { + /k_i ED + -1 k_i exp k_i factorial div + \psk@func@n k_i MoverN mul + x k_i exp mul L_n add + /L_n ED + } for + x \pst@number\psxunit mul L_n + %dup == %\pst@number\psyunit div + }% +}\ignorespaces} +% +\def\psLegendre{\@ifnextchar[{\psLegendre@i}{\psLegendre@i[]}}%% hv 20200115 +\def\psLegendre@i[#1](#2,#3){{%%% n + \pst@killglue% + \psplot[#1]{#2}{#3}{% + /P_n 0 def + \psk@func@n 0 eq { /P_1 1 def }{ \psk@func@n 1 eq { /P_1 x def } + { /P_0 1 def + /P_1 x def + 2 1 \psk@func@n { + /k_i ED + k_i dup add 1 sub x mul P_1 mul % (2n-1)*x*P_1 + k_i 1 sub P_0 mul sub % − ( n−1 ) P_{n-2}(x) + k_i div + /P_0 P_1 def + /P_1 ED + } for +%n Pn ( x ) = ( 2n − 1 ) P_{n−1}(x) − ( n−1 ) P_{n-2}(x) + } ifelse } ifelse + x \pst@number\psxunit mul P_1 + %dup == %\pst@number\psyunit div + }% +}\ignorespaces} +% \define@key[psset]{pst-func}{sigma}[0.5]{\def\psk@sigma{#1 }} \define@key[psset]{pst-func}{mue}[0]{\def\psk@mue{#1 }} \define@key[psset]{pst-func}{nue}[1]{\def\psk@nue{#1 }} |