Problem 46012. Find the zeros of the Bessel function of the first kind

Created by ChrisR

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{"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:hyperlink w:docLocation=\"https://mathworld.wolfram.com/BesselFunctionoftheFirstKind.html\"><w:r><w:t>Bessel functions</w:t></w:r></w:hyperlink><w:r><w:t> are important in many problems in mathematical physics--especially those with circular symmetry. Examples include the vibrations of a circular membrane and conduction of heat in a cylinder. Solving such problems usually requires finding the zeros of the Bessel functions and their derivatives. Like sine and cosine, the Bessel function of the first kind oscillates--as in the figure below. However, its zeros are not as easily predicted.</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>Find 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=\"k\"/></w:customXmlPr><w:r><w:t>k</w:t></w:r></w:customXml><w:r><w:t>th zero of the Bessel function of the first kind 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=\"nu\"/></w:customXmlPr><w:r><w:t>\\nu</w:t></w:r></w:customXml><w:r><w:t> and its derivative. For Bessel functions with </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=\"nu\"/></w:customXmlPr><w:r><w:t>\\nu</w:t></w:r></w:customXml><w:r><w:t> &gt; 0, skip the zero at </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=\"z\"/></w:customXmlPr><w:r><w:t>z</w:t></w:r></w:customXml><w:r><w:t> = 0. For the derivative of the Bessel function 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=\"nu\"/></w:customXmlPr><w:r><w:t>\\nu</w:t></w:r></w:customXml><w:r><w:t> = 0, start counting with the zero at </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=\"z\"/></w:customXmlPr><w:r><w:t>z</w:t></w:r></w:customXml><w:r><w:t> = 0.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"center\"/></w:pPr><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"-1\"/><w:attr w:name=\"width\" w:val=\"-1\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" 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<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: 569.467px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 284.733px; transform-origin: 407px 284.733px; vertical-align: baseline; "><div style="block-size: 84px; 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 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><a target='_blank' href = "https://mathworld.wolfram.com/BesselFunctionoftheFirstKind.html"><span style=""><span style="">Bessel functions</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: 305.617px 7.8px; transform-origin: 305.617px 7.8px; unicode-bidi: normal; "><span style=""> are important in many problems in mathematical physics--especially those with circular symmetry. Examples include the vibrations of a circular membrane and conduction of heat in a cylinder. Solving such problems usually requires finding the zeros of the Bessel functions and their derivatives. Like sine and cosine, the Bessel function of the first kind oscillates--as in the figure below. However, its zeros are not as easily predicted.</span></span></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: 27.2333px 7.8px; transform-origin: 27.2333px 7.8px; unicode-bidi: normal; "><span style="">Find the </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);">k</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: 165.683px 7.8px; transform-origin: 165.683px 7.8px; unicode-bidi: normal; "><span style="">th zero of the Bessel function of the first kind of order </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);">ν</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: 138.083px 7.8px; transform-origin: 138.083px 7.8px; unicode-bidi: normal; "><span style=""> and its derivative. For Bessel functions with </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);">ν</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: 30.15px 7.8px; transform-origin: 30.15px 7.8px; unicode-bidi: normal; "><span style=""> &gt; 0, skip the zero at </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);">z</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: 166.667px 7.8px; transform-origin: 166.667px 7.8px; unicode-bidi: normal; "><span style=""> = 0. For the derivative of the Bessel function of order </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);">ν</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: 109.1px 7.8px; transform-origin: 109.1px 7.8px; unicode-bidi: normal; "><span style=""> = 0, start counting with the zero at </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);">z</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: 13.8167px 7.8px; transform-origin: 13.8167px 7.8px; unicode-bidi: normal; "><span style=""> = 0.</span></span></div><div style="block-size: 425.467px; 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 212.733px; text-align: center; transform-origin: 384px 212.733px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline" 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" 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Last Solution submitted on Jan 20, 2023

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Solution 2653004

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Binbin Qi on 29 Nov 2020

Well done!

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Problem 46012. Find the zeros of the Bessel function of the first kind

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Problem 46012. Find the zeros of the Bessel function of the first kind

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