Problem 46025. Evaluate the gamma function

Created by ChrisR

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://mathworld.wolfram.com/GammaFunction.html\"><w:r><w:t>gamma function</w:t></w:r></w:hyperlink><w:r><w:t> 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</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>gamma</w:t></w:r><w:r><w:t>, but it accepts only real arguments.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Write a function that evaluates the gamma function for complex arguments.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

71 Solutions
11 Solvers

Last Solution submitted on Apr 17, 2021

Last 200 Solutions

Problem Comments

2 Comments

2 Comments

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.)

Solution Comments

Solution 2660459

2 Comments

2 Comments

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...

Problem Recent Solvers11

Problem Tags

complex numbers math special functions

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 46025. Evaluate the gamma function

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers11

Suggested Problems

More from this Author93

Problem Tags

Community Treasure Hunt

Problem 46025. Evaluate the gamma function

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers11

Suggested Problems

More from this Author93

Problem Tags

Community Treasure Hunt

Players