Several formulas can approximate the gamma function on the complex domain, but all of them have issues. Please, look at its plot before starting. Nonetheless, there is a trick that makes them all work; and you must find it (I've lost some time trying different formulas, adding more terms, but it is not the way to go).
I've found a 1968-paper by Wrench, Concerning Two Series for the Gamma Function, which gives us the 20th first terms of one formula for instance. https://www.ams.org/journals/mcom/1968-22-103/S0025-5718-1968-0237078-4/ (It would be more than enough if there weren't issues with all approximations.)
A clever and simple approach to deal with the pitfalls in the test suite. It can be easily extended to deal with other problematic values of the argument.
It took me a while to realize the same thing...
Rotate a Matrix by 90 degrees
Rotate input square matrix 90 degrees CCW without rot90
Sum the numbers on the main diagonal
Area of a triangle
Find the nearest prime number
Count trailing zeros in a primorial
Solve a Weird Calculator puzzle
Compute Khinchin's constant
Evaluate the logarithmic integral
Determine whether a square can be drawn on a grid of dots
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