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| ===== Pi function ===== | ===== Pi function ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#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 ==== | ||
| Line 12: | Line 12: | ||
| Wikipedia: [[http://en.wikipedia.org/wiki/Gamma_function|Gamma function]] | Wikipedia: [[http://en.wikipedia.org/wiki/Gamma_function|Gamma 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]] | ||
| + | === Equivalent to === | ||
| [[Gamma function]] | [[Gamma function]] | ||
