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higher_moments_of_the_stretched_exponential_function [2013/09/08 22:36] nikolaj |
higher_moments_of_the_stretched_exponential_function [2014/03/21 11:11] (current) |
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| ===== Higher moments of the stretched exponential function ===== | ===== Higher moments of the stretched exponential function ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#FFBB00: $\mathrm{it}: \mathbb R^3 \to \mathbb R$ | | + | | @#FFBB00: definiendum | @#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: definiendum | @#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 === | ||
| - | [[Function integral on ℝⁿ]], [[Complex exponents with positive real bases]] | ||
| === Context === | === Context === | ||
| + | [[Function integral on ℝⁿ]], [[Complex exponents with positive real bases]] | ||
| + | === Related === | ||
| [[Gamma function]] | [[Gamma function]] | ||
