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 ∙ العربية ∙ беларуская (тарашкевіца) ∙ български ∙ বাংলা ∙ català ∙ нохчийн ∙ čeština ∙ dansk ∙ Deutsch ∙ Ελληνικά ∙ English ∙ British English ∙ Esperanto ∙ español ∙ eesti ∙ euskara ∙ فارسی ∙ suomi ∙ français ∙ Frysk ∙ galego ∙ Alemannisch ∙ עברית ∙ हिन्दी ∙ hrvatski ∙ magyar ∙ հայերեն ∙ Bahasa Indonesia ∙ Ido ∙ italiano ∙ 日本語 ∙ ქართული ∙ 한국어 ∙ lietuvių ∙ македонски ∙ മലയാളം ∙ Bahasa Melayu ∙ မြန်မာဘာသာ ∙ norsk bokmål ∙ Plattdüütsch ∙ Nederlands ∙ norsk nynorsk ∙ norsk ∙ occitan ∙ polski ∙ prūsiskan ∙ português ∙ português do Brasil ∙ română ∙ русский ∙ sicilianu ∙ Scots ∙ slovenčina ∙ slovenščina ∙ српски / srpski ∙ svenska ∙ தமிழ் ∙ ไทย ∙ Türkçe ∙ татарча / tatarça ∙ українська ∙ vèneto ∙ Tiếng Việt ∙ 中文 ∙ 中文（中国大陆） ∙ 中文（简体） ∙ 中文（繁體） ∙ 中文（马来西亚） ∙ 中文（新加坡） ∙ 中文（臺灣） ∙ +/−

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.

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.