Gibbs phenomenon 10

Autor/Urheber:

Johannes Rössel (talk)

Shortlink:

https://dewiki.de/b/2a254a

Quelle:

Wikimedia Commons

Größe:

800 x 400 Pixel (2284 Bytes)

Beschreibung:

Picture of a function:

${\displaystyle \sin(x)+{\frac {1}{3}}\sin(3x)+{\frac {1}{5}}\sin(5x)+{\frac {1}{7}}\sin(7x)+{\frac {1}{9}}\sin(9x)}$

as the 5-th approximation (the first five terms) of the wave function:

${\displaystyle f\left(x\right)=\sum _{n=1}^{\infty }\,{\frac {1}{2n-1}}\sin((2n-1)x)}$

which is the Fourier series of the function:

${\displaystyle f(x)={\begin{cases}0&x=2n\pi \\\pi /4&2n\pi <x<(2n+1)\pi \\0&x=(2n+1)\pi \\-\pi /4&(2n+1)\pi <x<2(n+1)\pi \\\end{cases}}}$

Lizenz:

Public domain

Credit:

Eigenes Werk, drawn with Inkscape's function plotter

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