Problem 46066. Evaluate the logarithmic integral

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/Logarithmic_integral_function\"><w:r><w:t>logarithmic integral</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=\"li(x)\"/></w:customXmlPr><w:r><w:t>{\\rm li}(x)</w:t></w:r></w:customXml><w:r><w:t> plays a role in number theory because the related function </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=\"Li(x) = li(x) - li(2)\"/></w:customXmlPr><w:r><w:t>{\\rm Li}(x) = {\\rm li}(x) - {\\rm li}(2)</w:t></w:r></w:customXml><w:r><w:t> provides an estimate for the number of primes less than x. MATLAB's Symbolic Toolbox has the function</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/help/symbolic/sym.logint.html\"><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>logint</w:t></w:r></w:hyperlink><w:r><w:t>, but it is not available in basic MATLAB or Cody.</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 evaluate the logarithmic integral.</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>See also </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/46081-set-soldner-s-constant\"><w:r><w:t>Cody Problem 46081 \"Set Soldner's constant\"</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: 123px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 61.5px; transform-origin: 407px 61.5px; vertical-align: baseline; "><div style="block-size: 63px; 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 31.5px; text-align: left; transform-origin: 384px 31.5px; 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: 12.0667px 7.91667px; transform-origin: 12.0667px 7.91667px; 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: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; "><span style=""> </span></span><a target='_blank' href = "https://en.wikipedia.org/wiki/Logarithmic_integral_function"><span style=""><span style="">logarithmic integral</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: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; "><span style=""> </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAD0AAAAmCAYAAAB3c5OxAAACGklEQVRoge2YUbGsMAyGPw84wAAGUHAU1AEO1gEW0IAEPKwFNGCB8xAylD1QSNvdvXeGb4anQJq/NElbuLm5ubkx45YnFx1Q5nBUAQ3wBPqDd9zyTmHw65Agc1IicVYpDnpgBObl2RPtPHt70bcDhtjATqiQmJP+eEle0RUwpQZ1gkP+eBIh0TqI49ryHoFHakAXGFLHORN9FYf8ZUvux/KDxBy9onKJHrme9zlIGi+HaJ35OsGHlRZZWVFcyek+YAdpT7Nx3AKZrAd/J6tA2mQob5Mmek90iQiZDuyvjFxvU9ouB8//yFoLKrbjHm1wtPNEFbSQqOrE7vuISY+H579GhI+sf3kgXKyi0/JM1Jm9Jn7G/UltEJGN4fuJyI3QN0XDupQn7FtXTREz3xbde2NY++6AvYAC3xfdeGNYNzb/rWhtd6FKfYSla2xIFV1gO4X5OCRwzWtrTs98STTEVVE9JtaseT0avtfJzt6nr9hZbJYqWiDHQ13Ofl5rMeuRXdcRmlahdw4HzyFaz92h6tuy9uEn23Tw+3WLLPOzpd4SUfx0q6mDTWxnrWC7Y3q18/KubjCOmAlP4NktzitPjDWgRATtPc0F+x4d4Zysl+9De+mQ3UdXxidPdbuUyGr4RCAd6ef/bDTYKnAMNe+/hzPT8b4bFD2FmSv2JxjIe9Gv9G/ym42OvAG2mf29jZw3o/9UDt/c3Nx8hF8hL++a4KwTZwAAAABJRU5ErkJggg==" alt="li(x)" style="width: 30.5px; height: 19px;" width="30.5" height="19"></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: 184px 7.91667px; transform-origin: 184px 7.91667px; unicode-bidi: normal; "><span style=""> plays a role in number theory because the related function </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPwAAAAmCAYAAADgDvYuAAAFLElEQVR4nO2dXbXrIBCFt4c4iIEYiIIqqIM6qINaiIZKqIdaqIZaOOeBzuq0DTDAQH7WfGvlpbmHJDtsmAHCBQzDMAzDMAzDMAzDMAzDMIQcX4cWE4Besby9YXrX5wJgUCqrf5XXlRRyBHCOHDllnhJv7AhXYTTpAdyhJ/gSDHBa3gFcPf/G9C5jhDPSA07Hb7rX76mN4yT4mxFvn50Q126E0zjb9AOAw6uQP3Y8X7+PieUdWRmXhL+5JV5HygD3IrfW8/RwBn/greec4U3vfEY4HZ54azhn+ImdPwjLnhDuLEd8vlt+XBE29BHOr0X0XxeVPtjczaRUwAFO8JoVREWgheDvRcPwpvcvXEMNw1NE5mNk5d3w2+jQ7yHTT5A38F74BUvCMsoNJWHHA3lpQyq3RtepQcjwgOldCjdgKKSXmJ0aaF9k3MG9gxt+G90j4tEGL+cZuI4ILcNLoQcsGoQQcoB7ri2Emt/EDC/F9J4nZvgUJoTTpSOc4X3vgEcbsbSLxh2yaW34BxTCkhVfTwstw5ve82gZnnr3UCRwi5wH3r38U+F6QVoannqAopAkkQviIq4RDcOb3n60DH95lRFCMptyg8zwQHj2JopmDn+N3AgNhKTQwVXcM34rLuVZobxxiUqvgSSHN73zkebwd895gnLzUsjwEiNLGhkvJYbv4SoVH3QI3XCKODRFxUczeR404PO6vrlPCoFyBpN6xNcrSI6cyj+n5971bonP8COcDn+e8xzNZyVtJaE65fxZjapGDz9AVgFzQ9QzK3/Ee9STepu50U+N6/JKUXLkhIwhPfeqd0tiPfwpcp6XUTroR+9Turim6LpaIX2sAtJN5rSGvIKf4CpcysM+kRd2afXwObrG9Nyj3i2JGV6S41PDWJq+UOolLYfeT1ZksQXDA5+jmKnLQylM3RJLGh5orzdfbtoidVqL4cm8qTMb2VHUVgzP86rUeV4aENkSSxu+td48jWiROq3B8B3yR9z/kBlFbcXwPKdKXURihk+ntd4aPXxK/V2D4WnBTs6iqN0bnq9tTv2CKXfqZG2j9Cnnt6h3S5Y2fInZi2YHcgzf4feFxipgh7xcBXgvTaS8MjWnzG0N1zpKLzm/Rb1bomF4WnOQuuqtxOz83poZ/ozfL4NiFRDIG72lTy/5/GjKWmKq+EvOwy8xSg9sT++WaBg+Z7ScpjVDZj8gXGeKFjelGp4WYHw/pKQCXpE2ekuDGhRS8rySBpKuCLew9OKy1x4vhIbhTW8/GoYHnL7SQTf6kCk0CEr+CjUIlEokRwip38PzT/m+WxdJBaQVQqEHvuA973vHZ0jK54cvcKFRLNykZYgtvhbTgnrJUsOb3n6olyw1/ARZBETvgsY3fIckhbojY++BgV2AH6EboYO3QB0+p1Ro15w5qCKHBOTXmavMsd1gvrlDf1unmtDyWZ+epnc5Az53e/reoouWGfvOc6jhCEXH/PNXyREK1emdJg2kSva0Cx1UwUI5rq+SxVpEmp4JrdUOnedQD7X2DzmImJ6mdzmh6b+D4PwcD4QbuRRvxQZ4T2i3v4EKPRR27RAyYf1rumtjetfngHYm9G26uWpOKNy1Q8CI+vu4bQXTuz5X1E9l5mbHNsOEejuj0Nddax8pbonpXRea4ailQYuNSKtzg+5/ikBcK5W7dUzvutTao58ak63t/T/LBN3KclEub2+Y3nWhVaha5uzgGtRdmJ3QHOzYdMjTCNO7Pload4plGYZhGIZhGIZhGIZhGIaxFP/Ka2gIYQHNwgAAAABJRU5ErkJggg==" alt="Li(x) = li(x) - li(2)" style="width: 126px; height: 19px;" width="126" height="19"></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: 40.0667px 7.91667px; transform-origin: 40.0667px 7.91667px; unicode-bidi: normal; "><span style=""> provides an estimate for the number of primes less than x. MATLAB's Symbolic Toolbox has 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: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; "><span style=""> </span></span><a target='_blank' href = "https://www.mathworks.com/help/symbolic/sym.logint.html"><span style=""><span style="font-family: Menlo, Monaco, Consolas, &quot;Courier New&quot;, monospace; ">logint</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: 75px 7.91667px; transform-origin: 75px 7.91667px; unicode-bidi: normal; "><span style="">, but it is not available in basic MATLAB or Cody.</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: 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: 158.967px 7.91667px; transform-origin: 158.967px 7.91667px; unicode-bidi: normal; "><span style="">Write a function to evaluate the logarithmic integral.</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: 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: 29.1833px 7.91667px; transform-origin: 29.1833px 7.91667px; unicode-bidi: normal; "><span style="">See also </span></span><a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/46081-set-soldner-s-constant"><span style=""><span style="">Cody Problem 46081 "Set Soldner's constant"</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: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; "><span style="">.</span></span></div></div></div>

Solve

Solution Stats

63 Solutions
12 Solvers

Last Solution submitted on Jun 02, 2022

Last 200 Solutions

Problem Comments

Solution Comments

Solution 2756053

1 Comment

1 Comment

Binbin Qi on 24 Nov 2020

well done!

Problem Recent Solvers12

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 46066. Evaluate the logarithmic integral

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers12

Suggested Problems

More from this Author192

Problem Tags

Community Treasure Hunt

Problem 46066. Evaluate the logarithmic integral

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers12

Suggested Problems

More from this Author192

Problem Tags

Community Treasure Hunt

Players