Problem 46025. Evaluate the gamma function

Created by ChrisR

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Last Solution submitted on Sep 02, 2021

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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.)

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Solution 2660459

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ChrisR on 6 Jul 2020

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.

Rafael S.T. Vieira on 24 Oct 2020

It took me a while to realize the same thing...

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complex numbers math special functions

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Problem 46025. Evaluate the gamma function

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Problem 46025. Evaluate the gamma function

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