Complex Gamma? - 3

This is the same as $\Gamma(\Gamma(\pi+1$ ))

We can use the series approximation of the gamma function, twice

$\Gamma \left( z \right) ={ e }^{ -z }{ z }^{ z }\sqrt { \frac { 2\pi }{ z } } \left( 1+\frac { 1 }{ 12z } +\frac { 1 }{ 288{ z }^{ 2 } } -\frac { 139 }{ 51840{ z }^{ 3 } } -... \right)$

which will yield $1026.7787...$ which is accurate to two decimal places.

The constant $\pi$ might as well be any random irrational number insofar as computing the Gamma Function value of it. There are special numbers for which the Gamma Function has expressible values, but $\pi$ is not one of them.