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higher_moments_of_the_stretched_exponential_function [2013/09/08 22:36] nikolaj |
higher_moments_of_the_stretched_exponential_function [2013/09/09 16:27] nikolaj |
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==== Definition ==== | ==== Definition ==== | ||
| @#FFBB00: $\mathrm{it}: \mathbb R^3 \to \mathbb R$ | | | @#FFBB00: $\mathrm{it}: \mathbb R^3 \to \mathbb R$ | | ||
- | | @#FFBB00: $\langle \tau_K,\beta,n \rangle \mapsto \int_0^\infty\ \ t^{n-1}\ \mathrm{e}^{-(t/\tau_K)^\beta}$ | | + | | @#FFBB00: $\langle \tau_K,\beta,n \rangle \mapsto \int_0^\infty\ \ t^{n-1}\ \mathrm{e}^{-(t/\tau_K)^\beta}\ \mathrm d t$ | |
==== Discussion ==== | ==== Discussion ==== | ||
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^ $ \mathrm{it}(\tau_K,\beta,n)=\frac{\tau_K^n}{\beta}\Gamma(\frac{n}{\beta}) $ ^ | ^ $ \mathrm{it}(\tau_K,\beta,n)=\frac{\tau_K^n}{\beta}\Gamma(\frac{n}{\beta}) $ ^ | ||
=== Reference === | === Reference === | ||
- | Wikipedia: [[https://en.wikipedia.org/wiki/Stretched_exponential function|Stretched exponential_function]] | + | Wikipedia: [[https://en.wikipedia.org/wiki/Stretched_exponential function|Stretched exponential function]] |
==== Parents ==== | ==== Parents ==== | ||
=== Requirements === | === Requirements === |