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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) Both sides previous revision Previous revision 2013/09/09 16:27 nikolaj 2013/09/08 22:36 nikolaj 2013/09/08 22:36 nikolaj 2013/09/08 22:34 nikolaj created Next revision Previous revision 2013/09/09 16:27 nikolaj 2013/09/08 22:36 nikolaj 2013/09/08 22:36 nikolaj 2013/09/08 22:34 nikolaj created Line 1: Line 1: ===== 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: $\langle \tau_K,​\beta,​n \rangle \mapsto \int_0^\infty\ \ t^{n-1}\ \mathrm{e}^{-(t/​\tau_K)^\beta}\ \mathrm d t$ | + | @#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 ==== Line 8: Line 8: ^ $\mathrm{it}(\tau_K,​\beta,​n)=\frac{\tau_K^n}{\beta}\Gamma(\frac{n}{\beta})$ ^ ^ $\mathrm{it}(\tau_K,​\beta,​n)=\frac{\tau_K^n}{\beta}\Gamma(\frac{n}{\beta})$ ^ === 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]]