Image:KWW dist. function linear.png

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[edit] Summary

Description

Plot of the Kohlrausch-Williams-Watts distribution function
Source

Own work
Date

July 16,2006
Author

Mark Somoza
Permission
(Reusing this image)

GFDL and CC-BY-SA-2.5



G_{WW}(\tau)/\tau=\rho (\tau ) = - {{\tau _S } \over {\pi \tau ^2 }}\sum\limits_{k = 0}^\infty {{{( - 1)^k } \over {k!}}\sin (\pi \beta k)\Gamma (\beta k + 1)\left( {{\tau \over {\tau _S }}} \right)} ^{\beta k + 1}

Calculated with Mathematica using:

l[t\_]: = - {{{\rm tww}} \over {{\rm Pi*t}}}{\rm *NSum[}{{{\rm ( - 1)}^{\rm k} } \over {{\rm k!}}}{\rm Sin[Pi*beta*k]*Gamma[beta*k + 1]*}\left( {{{\rm t} \over {{\rm tww}}}} \right)^{{\rm beta*k + 1}},\,
{\rm \{ k, 0, 5000\} , WorkingPrecision - > 50, NSumTerms - > 5000]} \,


Based on:

  • Lindsey, C. P. and Patterson, G. D. (1980). "Detailed comparison of the Williams-Watts and Cole-Davidson functions". Journal of Chemical Physics 73: 3348-3357.

[edit] Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation license, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation license".

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current15:10, 16 July 20062,528×1,820 (169 KB)Somoza ({{Information |Description= Plot of the Kohlrausch-Williams-Watts distribution function |Source= Own work |Date= July 16,2006 |Author= Mark Somoza |Permission= GFDL and CC-BY-SA-2.5 |other_versions= }})
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