Problem 46025. Evaluate the gamma function

Created by ChrisR

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></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:jc w:val=\"left\"/></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>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 93.3333px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 46.6667px; transform-origin: 407.5px 46.6667px; vertical-align: baseline; "><div style="block-size: 63.3333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 31.6667px; text-align: left; transform-origin: 384.5px 31.6667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.0583px 7.66667px; transform-origin: 12.0583px 7.66667px; unicode-bidi: normal; "><span style="">The</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.66667px; transform-origin: 1.94167px 7.66667px; unicode-bidi: normal; "><span style=""> </span></span><a target='_blank' href = "https://mathworld.wolfram.com/GammaFunction.html"><span style=""><span style="">gamma function</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 302.642px 7.66667px; transform-origin: 302.642px 7.66667px; unicode-bidi: normal; "><span style=""> 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</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.66667px; transform-origin: 1.94167px 7.66667px; unicode-bidi: normal; "><span style=""> </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.25px 7.66667px; transform-origin: 19.25px 7.66667px; unicode-bidi: normal; "><span style="font-family: Menlo, Monaco, Consolas, &quot;Courier New&quot;, monospace; perspective-origin: 19.25px 8px; transform-origin: 19.25px 8px; ">gamma</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.66667px; transform-origin: 3.88333px 7.66667px; unicode-bidi: normal; "><span style="">, but it accepts only real arguments.</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 232.467px 7.66667px; transform-origin: 232.467px 7.66667px; unicode-bidi: normal; "><span style="">Write a function that evaluates the gamma function for complex arguments.</span></span></div></div></div>

Solve

Solution Stats

94 Solutions
15 Solvers

Last Solution submitted on May 01, 2023

Last 200 Solutions

Problem Comments

3 Comments

3 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.)

Nikolaos Nikolaou on 24 Dec 2021

lol that was fun xD

Solution Comments

Show comments

Problem Recent Solvers15

Problem Tags

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 Solvers15

Suggested Problems

More from this Author206

Problem Tags

Community Treasure Hunt

Problem 46025. Evaluate the gamma function

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers15

Suggested Problems

More from this Author206

Problem Tags

Community Treasure Hunt

Players