Problem 55335. Generate Bernoulli polynomials

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 Bernoulli polynomial </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=\"B_n(x)\"/></w:customXmlPr><w:r><w:t>B_n(x)</w:t></w:r></w:customXml><w:r><w:t> is a polynomial of order </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=\"n\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t> with the properties that </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=\"B_0(x) = 1\"/></w:customXmlPr><w:r><w:t>B_0(x) = 1</w:t></w:r></w:customXml><w:r><w:t> and for </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=\"n &gt; 0\"/></w:customXmlPr><w:r><w:t>n &gt; 0</w:t></w:r></w:customXml><w:r><w:t> </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=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"B'_n(x) = n B_{n-1}(x)\"/></w:customXmlPr><w:r><w:t>B\\prime_n(x) = nB_{n-1}(x)</w:t></w:r></w:customXml><w:r><w:t>,</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>where the prime denotes differentiation with respect to </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=\"x\"/></w:customXmlPr><w:r><w:t>x</w:t></w:r></w:customXml><w:r><w:t>, and</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=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"Integral[B_n(x),{x,0,1}] = 0\"/></w:customXmlPr><w:r><w:t>\\int_0^1 B_n(x) = 0</w:t></w:r></w:customXml><w:r><w:t>.</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>Therefore, </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=\"B_1(x) = x-1/2\"/></w:customXmlPr><w:r><w:t>B_1(x) = x – ½</w:t></w:r></w:customXml><w:r><w:t>, </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=\"B_2(x) = x^2 – x + 1/6\"/></w:customXmlPr><w:r><w:t>B_2(x) = x^2 – x + 1/6</w:t></w:r></w:customXml><w:r><w:t>, </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=\"B_3(x) = x^3 – 3 x^2/2 + x/2\"/></w:customXmlPr><w:r><w:t>B_3(x) = x^3 – 3 x^2/2 + x/2</w:t></w:r></w:customXml><w:r><w:t>, etc. Notice that </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=\"B_n(0)\"/></w:customXmlPr><w:r><w:t>B_n(0)</w:t></w:r></w:customXml><w:r><w:t> is the </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=\"n\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t>th </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/45831\"><w:r><w:rPr><w:u/></w:rPr><w:t>Bernoulli number</w:t></w:r></w:hyperlink><w:r><w:t>.</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 to generate the Bernoulli polynomial of order </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=\"n\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t>. Use MATLAB's approach for specifying the coefficients. For example, the function should return [1 -1/2] for </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=\"n = 1\"/></w:customXmlPr><w:r><w:t>n = 1</w:t></w:r></w:customXml><w:r><w:t> and [1 -1 1/6] for </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=\"n = 2\"/></w:customXmlPr><w:r><w:t>n=2</w:t></w:r></w:customXml><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: 201px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 100.5px; transform-origin: 407px 100.5px; vertical-align: baseline; "><div style="block-size: 22px; 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 11px; text-align: left; transform-origin: 384px 11px; 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: 78.5917px 8px; transform-origin: 78.5917px 8px; unicode-bidi: normal; ">The Bernoulli polynomial <img src="data:image/png;base64,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" alt="B_n(x)" style="width: 36.5px; height: 20px;" width="36.5" height="20"><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: 76.2417px 8px; transform-origin: 76.2417px 8px; unicode-bidi: normal; "> is a polynomial of order n<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: 74.675px 8px; transform-origin: 74.675px 8px; unicode-bidi: normal; "> with the properties that <img src="data:image/png;base64,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" alt="B_0(x) = 1" style="width: 62.5px; height: 20px;" width="62.5" height="20"><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: 25.6667px 8px; transform-origin: 25.6667px 8px; unicode-bidi: normal; "> and for <img src="data:image/png;base64,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" alt="n > 0" style="width: 36.5px; height: 18px;" width="36.5" height="18"><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 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; "> </div><div style="block-size: 22px; 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 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img src="data:image/png;base64,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" alt="B'_n(x) = n B_{n-1}(x)" style="width: 113.5px; height: 20px;" width="113.5" height="20"><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 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; ">,</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: 169.858px 8px; transform-origin: 169.858px 8px; unicode-bidi: normal; ">where the prime denotes differentiation with respect to x<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 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; ">, and</div><div style="block-size: 27px; 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 13.5px; text-align: left; transform-origin: 384px 13.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img src="data:image/png;base64,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" alt="Integral[B_n(x),{x,0,1}] = 0" style="width: 80px; height: 27px;" width="80" height="27"><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 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; ">.</div><div style="block-size: 22px; 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 11px; text-align: left; transform-origin: 384px 11px; 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: 34.225px 8px; transform-origin: 34.225px 8px; unicode-bidi: normal; ">Therefore, <img src="data:image/png;base64,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" alt="B_1(x) = x-1/2" style="width: 81px; height: 20px;" width="81" height="20"><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 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; ">, <img src="data:image/png;base64,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" alt="B_2(x) = x^2 – x + 1/6" style="width: 121.5px; height: 21px;" width="121.5" height="21"><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 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; ">, <img src="data:image/png;base64,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" alt="B_3(x) = x^3 – 3 x^2/2 + x/2" style="width: 149px; height: 21px;" width="149" height="21"><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: 52.4917px 8px; transform-origin: 52.4917px 8px; unicode-bidi: normal; ">, etc. Notice that <img src="data:image/png;base64,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" alt="B_n(0)" style="width: 36.5px; height: 20px;" width="36.5" height="20"><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: 20.6083px 8px; transform-origin: 20.6083px 8px; unicode-bidi: normal; "> is the n<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: 7.775px 8px; transform-origin: 7.775px 8px; unicode-bidi: normal; ">th <a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/45831">Bernoulli number</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 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; ">.</div><div style="block-size: 42px; 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 21px; text-align: left; transform-origin: 384px 21px; 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: 190.092px 8px; transform-origin: 190.092px 8px; unicode-bidi: normal; ">Write a function to generate the Bernoulli polynomial of order n<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: 188.658px 8px; transform-origin: 188.658px 8px; unicode-bidi: normal; ">. Use MATLAB's approach for specifying the coefficients. For example, the function should return [1 -1/2] for <img src="data:image/png;base64,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" alt="n = 1" style="width: 36.5px; height: 18px;" width="36.5" height="18"><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: 55.2167px 8px; transform-origin: 55.2167px 8px; unicode-bidi: normal; "> and [1 -1 1/6] for <img src="data:image/png;base64,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" alt="n = 2" style="width: 36.5px; height: 18px;" width="36.5" height="18"><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 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; ">.</div></div></div>

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Last Solution submitted on Sep 04, 2022

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Solution 8994655

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2 Comments

Ramon Villamangca on 4 Sep 2022

Hi Chris,
I appreciate if you can check why my function fails for m==14. Thanks.

ChrisR on 17 Sep 2022

Ramon, your values are within 1e-11 of mine, so I loosened the tolerance.

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Problem 55335. Generate Bernoulli polynomials

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