File:Weierstrass.png

Summary[edit]

DescriptionWeierstrass.png	English: The graph of a function f(x) (black) and its generalized Weierstrass transforms for t=0.2 (red), t=1 (green) and t=3 (blue). The standard Weierstrass transfrom F(x) is the case t=1, the green graph.
Date	May 2008
Source	Own work
Author	AxelBoldt
Other versions	File:Weierstrass transform.svg is a vector version of this file. It should be used in place of this PNG file when not inferior. File:Weierstrass.png → File:Weierstrass transform.svg For more information, see Help:SVG. In other languages Alemannisch ∙ Bahasa Indonesia ∙ Bahasa Melayu ∙ British English ∙ català ∙ čeština ∙ dansk ∙ Deutsch ∙ eesti ∙ English ∙ español ∙ Esperanto ∙ euskara ∙ français ∙ Frysk ∙ galego ∙ hrvatski ∙ Ido ∙ italiano ∙ lietuvių ∙ magyar ∙ Nederlands ∙ norsk bokmål ∙ norsk nynorsk ∙ occitan ∙ Plattdüütsch ∙ polski ∙ português ∙ português do Brasil ∙ română ∙ Scots ∙ sicilianu ∙ slovenčina ∙ slovenščina ∙ suomi ∙ svenska ∙ Tiếng Việt ∙ Türkçe ∙ vèneto ∙ Ελληνικά ∙ беларуская (тарашкевіца) ∙ български ∙ македонски ∙ нохчийн ∙ русский ∙ српски / srpski ∙ татарча/tatarça ∙ українська ∙ ქართული ∙ հայերեն ∙ বাংলা ∙ தமிழ் ∙ മലയാളം ∙ ไทย ∙ 한국어 ∙ 日本語 ∙ 简体中文 ∙ 繁體中文 ∙ עברית ∙ العربية ∙ فارسی ∙ +/−

File was created with the following Maple 6 code:

> W := (f,t,x) -> 1/sqrt(4*t*Pi)*int(f(x-y)*exp(-y^2/4/t),y=-infinity..infinity);
> f:= x-> piecewise(x<0 or x>10,0,x<5,5,5-2*(x-5));
> plotsetup(ps,plotoutput=`weierstrass.ps`,
    plotoptions=`width=8in,height=6in,portrait,color,noborder`);
> plot([f(x),W(f,0.2,x),W(f,1,x),W(f,3,x)],x=-10..20,
    axes=boxed,color=[black,red,green,blue],thickness=[2,3,3,3]);

and then converted from Postscript to PNG using GraphicsMagic.

Licensing[edit]

I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.