lgamma() [4/7]

double stan::math::lgamma ( double  x )

inline

Return the natural logarithm of the gamma function applied to the specified argument.

\[ \mbox{lgamma}(x) = \begin{cases} \textrm{error} & \mbox{if } x\in \{\dots, -3, -2, -1, 0\}\\ \ln\Gamma(x) & \mbox{if } x\not\in \{\dots, -3, -2, -1, 0\}\\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{lgamma}(x)}{\partial x} = \begin{cases} \textrm{error} & \mbox{if } x\in \{\dots, -3, -2, -1, 0\}\\ \Psi(x) & \mbox{if } x\not\in \{\dots, -3, -2, -1, 0\}\\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters

x

argument

Returns

natural logarithm of the gamma function applied to argument

Definition at line 63 of file lgamma.hpp.