Problem 45976. Evaluate the Struve 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://en.wikipedia.org/wiki/Struve_function\"><w:r><w:t>Struve function</w:t></w:r></w:hyperlink><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=\"H_p(x)\"/></w:customXmlPr><w:r><w:t>{\\bf H}_p(x)</w:t></w:r></w:customXml><w:r><w:t> is a solution to an inhomogeneous form of Bessel's equation:</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>        </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/><w:attr w:name=\"altTextString\" w:val=\"Differential equation from the Wikipedia link\"/></w:customXmlPr><w:r><w:t>x^2\\frac{d^2y}{dx^2}+x\\frac{dy}{dx}+(x^2-p^2)y=\\frac{4(x/2)^{p+1}}{\\sqrt{\\pi}\\Gamma(p+1/2)}</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>The Struve function appears in applications of optics and loudspeaker design. I encountered it in developing a model of turbulence in a strongly stratified fluid (e.g., a lake with a large temperature difference).</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>Evaluate the Struve function</w:t></w:r><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=\"H_p(x)\"/></w:customXmlPr><w:r><w:t>{\\bf H}_p(x)</w:t></w:r></w:customXml><w:r><w:t> for given values of the 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=\"p\"/></w:customXmlPr><w:r><w:t>p</w:t></w:r></w:customXml><w:r><w:t> and argument </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>.</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: 151.583px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 75.7917px; transform-origin: 407px 75.7917px; vertical-align: baseline; "><div style="block-size: 21.8167px; 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 10.9083px; text-align: left; transform-origin: 384px 10.9083px; 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 7.79167px; transform-origin: 12.0583px 7.79167px; 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 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; "><span style=""> </span></span><a target='_blank' href = "https://en.wikipedia.org/wiki/Struve_function"><span style=""><span style="">Struve 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: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; "><span style=""> </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" alt="H_p(x)" style="width: 40px; height: 20px;" width="40" height="20"></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: 190.383px 7.79167px; transform-origin: 190.383px 7.79167px; unicode-bidi: normal; "><span style=""> is a solution to an inhomogeneous form of Bessel's equation:</span></span></div><div style="block-size: 38.95px; 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 19.475px; text-align: left; transform-origin: 384px 19.475px; 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: 15.5333px 7.79167px; transform-origin: 15.5333px 7.79167px; unicode-bidi: normal; "><span style="">        </span></span><span style="vertical-align:-17px"><img src="data:image/png;base64,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" alt="Differential equation from the Wikipedia link" style="width: 271.5px; height: 39px;" width="271.5" height="39"></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: 370.333px 7.79167px; transform-origin: 370.333px 7.79167px; unicode-bidi: normal; "><span style="">The Struve function appears in applications of optics and loudspeaker design. I encountered it in developing a model of turbulence in a strongly stratified fluid (e.g., a lake with a large temperature difference).</span></span></div><div style="block-size: 21.8167px; 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 10.9083px; text-align: left; transform-origin: 384px 10.9083px; 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: 87.5167px 7.79167px; transform-origin: 87.5167px 7.79167px; unicode-bidi: normal; "><span style="">Evaluate the Struve 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 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; "><span style=""> </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" alt="H_p(x)" style="width: 40px; height: 20px;" width="40" height="20"></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: 90.625px 7.79167px; transform-origin: 90.625px 7.79167px; unicode-bidi: normal; "><span style=""> for given values of the 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);">p</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: 47.0667px 7.79167px; transform-origin: 47.0667px 7.79167px; unicode-bidi: normal; "><span style=""> and argument </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);">x</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 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; "><span style="">.</span></span></div></div></div>

Solve

Solution Stats

30 Solutions
15 Solvers

Last Solution submitted on Dec 24, 2021

Last 200 Solutions

Problem Comments

1 Comment

1 Comment

ChrisR on 2 Jan 2021

I added a test to prevent lookup solutions.

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 45976. Evaluate the Struve function

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers15

Suggested Problems

More from this Author161

Problem Tags

Community Treasure Hunt

Problem 45976. Evaluate the Struve function

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers15

Suggested Problems

More from this Author161

Problem Tags

Community Treasure Hunt

Players