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-rw-r--r--Master/texmf-dist/doc/generic/pst-func/Changes2
-rw-r--r--Master/texmf-dist/doc/generic/pst-func/README.md4
-rw-r--r--Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdfbin3956145 -> 3889616 bytes
-rw-r--r--Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex69
-rw-r--r--Master/texmf-dist/tex/generic/pst-func/pst-func.tex48
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
index 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
Binary files differ
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 }}