LogGammaD function
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Namespace: Microsoft.Quantum.Math
Package: Microsoft.Quantum.Standard
Returns the natural logarithm of the gamma function (aka the log-gamma function).
function LogGammaD (x : Double) : Double
Description
The gamma function $\Gamma(x)$ generalizes the factorial function to the positive real numbers and is defined as $$ \begin{align} \Gamma(x) \mathrel{:=} \int_0^{\infty} t^{x - 1} e^{-t} dt. \end{align} $$
The gamma function has the property that for all positive real numbers $x$, $\Gamma(x + 1) = x \Gamma(x)$, such that the factorial function is a special case of $\Gamma$, $n! = \Gamma(n + 1)$ for all natural numbers $n$.
Input
x : Double
The point $x$ at which the log-gamma function is to be evaluated.
Output : Double
The value $\ln \Gamma(x)$.
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