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pi_function [2013/09/08 18:30] nikolaj |
pi_function [2013/09/09 15:47] nikolaj |
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| === Theorems === | === Theorems === | ||
| ^ $n\in\mathbb N \implies \Pi(n)=n! $ ^ | ^ $n\in\mathbb N \implies \Pi(n)=n! $ ^ | ||
| - | ^ $\Pi(x)\cdot \Pi(x+1)=\frac{\pi}{\sin(\pi\ x)} $ ^ | + | ^ $\Pi(z)\cdot \Pi(-z)=\frac{\tau\ z/2}{\sin(\tau\ z/2)} $ ^ |
| === Reference === | === Reference === | ||
| Wikipedia: [[http://en.wikipedia.org/wiki/Gamma_function|Gamma function]] | Wikipedia: [[http://en.wikipedia.org/wiki/Gamma_function|Gamma function]] | ||
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| === Requirements === | === Requirements === | ||
| [[Function integral on ℝⁿ]], [[Complex exponents with positive real bases]] | [[Function integral on ℝⁿ]], [[Complex exponents with positive real bases]] | ||
| - | === Context === | + | === Equivalent to === |
| [[Gamma function]] | [[Gamma function]] | ||
