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pi_function [2013/09/09 15:47]
nikolaj
pi_function [2015/01/12 18:19]
nikolaj
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 ===== Pi function ===== ===== Pi function =====
-==== Definition ​==== +==== Function ​==== 
-| @#FFBB00: $\Pi: \mathbb C\setminus\{-k\ |\ k\in\mathbb N^*\}\to \mathbb N$ | +| @#FFBB00: definiendum ​| @#FFBB00: $\Pi: \mathbb C\setminus\{-k\ |\ k\in\mathbb N^*\}\to \mathbb N$ | 
-| @#FFBB00: $\Pi(z) := \begin{cases} \int_0^\infty\ \ t^{z}\ \mathrm{e}^{-t}\ \mathrm d t & \mathrm{if}\ \mathrm{Re}(z)>​0 \\\\ \frac{1}{z+1}\Pi(z+1) & \mathrm{else} \end{cases}$ |+| @#FFBB00: definiendum ​| @#FFBB00: $\Pi(z) := \begin{cases} \int_0^\infty\ \ t^{z}\ \mathrm{e}^{-t}\ \mathrm d t & \mathrm{if}\ \mathrm{Re}(z)>​0 \\\\ \frac{1}{z+1}\Pi(z+1) & \mathrm{else} \end{cases}$ |
  
 ==== Discussion ==== ==== Discussion ====
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 Wikipedia: [[http://​en.wikipedia.org/​wiki/​Gamma_function|Gamma function]] Wikipedia: [[http://​en.wikipedia.org/​wiki/​Gamma_function|Gamma function]]
 ==== Parents ==== ==== Parents ====
-=== Requirements ​===+=== Context ​===
 [[Function integral on ℝⁿ]], [[Complex exponents with positive real bases]] [[Function integral on ℝⁿ]], [[Complex exponents with positive real bases]]
 === Equivalent to === === Equivalent to ===
 [[Gamma function]] [[Gamma function]]
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