===== Higher moments of the stretched exponential function =====
==== Set ====
| @#FFBB00: definiendum | @#FFBB00: $\mathrm{it}: \mathbb R^3 \to \mathbb R$ |
| @#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 ====
=== Theorems ===
^ $ \mathrm{it}(\tau_K,\beta,n)=\frac{\tau_K^n}{\beta}\Gamma(\frac{n}{\beta}) $ ^
=== Reference ===
Wikipedia: [[https://en.wikipedia.org/wiki/Stretched_exponential function|Stretched exponential function]]
==== Parents ====
=== Context ===
[[Function integral on ℝⁿ]], [[Complex exponents with positive real bases]]
=== Related ===
[[Gamma function]]