Problem 46025. Evaluate the gamma function

Created by ChrisR

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The gamma function is a generalization of the factorial, and it appears in many applications such as evaluating certain integrals, working with probability distributions, and evaluating fractional derivatives. MATLAB includes the function gamma, but it accepts only real arguments.
Write a function that evaluates the gamma function for complex arguments.

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Last Solution submitted on Sep 05, 2024

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Rafael S.T. Vieira on 24 Oct 2020

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).

Rafael S.T. Vieira on 24 Oct 2020

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.)

Nikolaos Nikolaou on 24 Dec 2021

lol that was fun xD

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Problem 46025. Evaluate the gamma function

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Problem 46025. Evaluate the gamma function

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