Problem 51975. Compute a sum of Ramanujan

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>Srinivasa Ramanujan defined the following function:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/><w:attr w:name=\"altTextString\" w:val=\"phi(a) = 1+2 Sum[1/((a k)^3 - a k),{k,1,infinity}]\"/></w:customXmlPr><w:r><w:t>\\phi(a) = 1+2\\sum_{k=1}^\\infty\\frac{1}{(a k)^3 – a k}</w:t></w:r></w:customXml></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 to compute </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"phi(a)\"/></w:customXmlPr><w:r><w:t>\\phi(a)</w:t></w:r></w:customXml><w:r><w:t> for various values of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"a\"/></w:customXmlPr><w:r><w:t>a</w:t></w:r></w:customXml><w:r><w:t>. See also Cody Problems </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/45960\"><w:r><w:rPr><w:u/></w:rPr><w:t>45960</w:t></w:r></w:hyperlink><w:r><w:t> and </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/46000-compute-the-harmonic-numbers\"><w:r><w:rPr><w:u/></w:rPr><w:t>46000</w:t></w:r></w:hyperlink><w:r><w:t>.</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: 105px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52.5px; transform-origin: 407px 52.5px; vertical-align: baseline; "><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: 384px 10.5px; text-align: left; transform-origin: 384px 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: 160.675px 7.79167px; transform-origin: 160.675px 7.79167px; unicode-bidi: normal; "><span style="">Srinivasa Ramanujan defined the following function:</span></span></div><div style="block-size: 45px; 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: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-17px"><img src="data:image/png;base64,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" alt="phi(a) = 1+2 Sum[1/((a k)^3 - a k),{k,1,infinity}]" style="width: 162.5px; height: 45px;" width="162.5" height="45"></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: 384px 10.5px; text-align: left; transform-origin: 384px 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: 86.9917px 7.79167px; transform-origin: 86.9917px 7.79167px; unicode-bidi: normal; "><span style="">Write a function to compute </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" alt="phi(a)" style="width: 32.5px; height: 18.5px;" width="32.5" height="18.5"></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: 66.5083px 7.79167px; transform-origin: 66.5083px 7.79167px; unicode-bidi: normal; "><span style=""> for various values of </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">a</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: 82.85px 7.79167px; transform-origin: 82.85px 7.79167px; unicode-bidi: normal; "><span style="">. See also Cody Problems </span></span><a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/45960"><span style=""><span style="text-decoration: underline; text-decoration-line: underline; ">45960</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: 15.5583px 7.79167px; transform-origin: 15.5583px 7.79167px; unicode-bidi: normal; "><span style=""> and </span></span><a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/46000-compute-the-harmonic-numbers"><span style=""><span style="text-decoration: underline; text-decoration-line: underline; ">46000</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: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; "><span style="">.</span></span></div></div></div>

Solve

Solution Stats

26 Solutions
10 Solvers

Last Solution submitted on Oct 28, 2022

Last 200 Solutions

Problem Comments

Problem Recent Solvers10

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 51975. Compute a sum of Ramanujan

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers10

Suggested Problems

More from this Author190

Problem Tags

Community Treasure Hunt

Problem 51975. Compute a sum of Ramanujan

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers10

Suggested Problems

More from this Author190

Problem Tags

Community Treasure Hunt

Players

WeChat