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pi_function [2014/03/21 11:11]
127.0.0.1 external edit
pi_function [2015/01/12 18:19] (current)
nikolaj
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 ===== Pi function ===== ===== Pi function =====
-==== Set ====+==== Function ​====
 | @#FFBB00: definiendum | @#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: definiendum | @#FFBB00: $\Pi(z) := \begin{cases} \int_0^\infty\ \ t^{z}\ \mathrm{e}^{-t}\ \mathrm d t & \mathrm{if}\ \mathrm{Re}(z)>​0 \\\\ \frac{1}{z+1}\Pi(z+1) & \mathrm{else} \end{cases}$ | | @#FFBB00: definiendum | @#FFBB00: $\Pi(z) := \begin{cases} \int_0^\infty\ \ t^{z}\ \mathrm{e}^{-t}\ \mathrm d t & \mathrm{if}\ \mathrm{Re}(z)>​0 \\\\ \frac{1}{z+1}\Pi(z+1) & \mathrm{else} \end{cases}$ |
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