Problem 46043. Evaluate the generalized hypergeometric 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/Generalized_hypergeometric_function\"><w:r><w:t>generalized hypergeometric function</w:t></w:r></w:hyperlink><w:r><w:t> is defined as</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=\"(See the definition at the Wikipedia link)\"/></w:customXmlPr><w:r><w:t>_pF_q(a_1,\\ldots,a_p; c_1,\\ldots,c_q; x) = \\sum_{n=0}^\\infty \\frac{(a_1)_n\\cdots (a_p)_n}{(c_1)_n\\cdots (c_q)_n}\\frac{x^n}{n!}</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 numbers</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=\"p\"/></w:customXmlPr><w:r><w:t>p</w:t></w:r></w:customXml><w:r><w:t> and</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=\"q\"/></w:customXmlPr><w:r><w:t>q</w:t></w:r></w:customXml><w:r><w:t> are the numbers of values</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=\"a\"/></w:customXmlPr><w:r><w:t>a</w:t></w:r></w:customXml><w:r><w:t> and</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=\"b\"/></w:customXmlPr><w:r><w:t>b</w:t></w:r></w:customXml><w:r><w:t> in the numerator and denominator (respectively), and the Pochhammer symbol </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)_n\"/></w:customXmlPr><w:r><w:t>(a)_n</w:t></w:r></w:customXml><w:r><w:t> is defined by</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=\"(a)_n = a*(a+1)*(a+2)...(a+n-1)\"/></w:customXmlPr><w:r><w:t>(a)_n = a(a+1)\\cdots (a+n-1)</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>Many other functions can be expressed in terms of the generalized hypergeometric function. For example,</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=\"exp(x) = pFq([],[],x)\"/></w:customXmlPr><w:r><w:t>e^x = {}_0F_0(-,-,x)</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>       </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=\"cos(x0 = pFq([],1/2,-x^2/4)\"/></w:customXmlPr><w:r><w:t>\\cos(x) = {}_0F_1\\left(-,\\frac{1}{2},-\\frac{x^2}{4}\\right)</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>       </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=\"besselj(0,x) = pFq([],1,-x^2/4)\"/></w:customXmlPr><w:r><w:t>J_0(x) = {}_0F_1\\left(-,1,-\\frac{x^2}{4}\\right)</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>where the dash means that the list of parameters is empty. The generalized hypergeometric function can be computed with</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>hypergeom</w:t></w:r><w:r><w:t> from the Symbolic Math Toolbox, but it is not available in Cody or basic MATLAB.</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 generalized hypergeometric function.</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: 395.9px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 197.95px; transform-origin: 407px 197.95px; 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: 12.0667px 7.8px; transform-origin: 12.0667px 7.8px; 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 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; "><span style=""> </span></span><a target='_blank' href = "https://en.wikipedia.org/wiki/Generalized_hypergeometric_function"><span style=""><span style="">generalized hypergeometric 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: 41.2333px 7.8px; transform-origin: 41.2333px 7.8px; unicode-bidi: normal; "><span style=""> is defined as</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="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: 13.6px 7.8px; transform-origin: 13.6px 7.8px; unicode-bidi: normal; "><span style="">       </span></span><span style="vertical-align:-17px"><img src="data:image/png;base64,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" alt="(See the definition at the Wikipedia link)" style="width: 301px; height: 45px;" width="301" height="45"></span></div><div style="block-size: 42.8167px; 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 21.4167px; text-align: left; transform-origin: 384px 21.4167px; 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: 41.2333px 7.8px; transform-origin: 41.2333px 7.8px; unicode-bidi: normal; "><span style="">The numbers</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 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; "><span style=""> </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: 13.6167px 7.8px; transform-origin: 13.6167px 7.8px; unicode-bidi: normal; "><span style=""> and</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 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; "><span style=""> </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);">q</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 7.8px; transform-origin: 82.85px 7.8px; unicode-bidi: normal; "><span style=""> are the numbers of values</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 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; "><span style=""> </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: 13.6167px 7.8px; transform-origin: 13.6167px 7.8px; unicode-bidi: normal; "><span style=""> and</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 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; "><span style=""> </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);">b</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: 180.1px 7.8px; transform-origin: 180.1px 7.8px; unicode-bidi: normal; "><span style=""> in the numerator and denominator (respectively), and the Pochhammer symbol </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" alt="(a)_n" style="width: 27px; height: 20px;" width="27" 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: 41.2333px 7.8px; transform-origin: 41.2333px 7.8px; unicode-bidi: normal; "><span style=""> is defined by</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 10.9167px; text-align: left; transform-origin: 384px 10.9167px; 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: 13.6px 7.8px; transform-origin: 13.6px 7.8px; unicode-bidi: normal; "><span style="">       </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" alt="(a)_n = a*(a+1)*(a+2)...(a+n-1)" style="width: 184px; height: 20px;" width="184" height="20"></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: 327.917px 7.8px; transform-origin: 327.917px 7.8px; unicode-bidi: normal; "><span style="">Many other functions can be expressed in terms of the generalized hypergeometric function. For example,</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 10.9167px; text-align: left; transform-origin: 384px 10.9167px; 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: 13.6px 7.8px; transform-origin: 13.6px 7.8px; unicode-bidi: normal; "><span style="">       </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANEAAAAqCAYAAAAtb741AAAE0UlEQVR4nO2cy5WjMBBFXw5k4ARIgAiIgPVsnIEzIAXHQAjOgRQcg1PoWYg3lHXERx9LHnXdc1i0oUEWqt+TZEBRFEVRFEVRFEVRFEVRFEVRFCUrdwBD6UZUyANAX7oRv4Uu4mgin60G9FkeKNy/LcxAIQ3SDJxvowNwBfAC8COOJ8xLkId9TQx3AGPkPZR9GgAz3sdxFi4wg2qGGSgdjEE9l79vuRuUiQdW45h2ruuWa+aIZw0w/VmbQ/pGOhjnV6SvrzCDZYQZYJcSjciIjDLXg2sfCI8izfIsTePycce+Y/wYLdZBVXuBdsF7mnbkMGJy7RtMFFLywbGcPa0D1tqgdhh1z37fHmGRmVHoKNIp6ZlhIlJWGqx1UO2p3ITViFwd3cB4s1iG5Rkp7qX4cYPp+2S1EZW2vfA2YRUXas/fZT3kSl1vSOPFpuVZSjgUumwu2FePKQhFlyYDjGHMMIUx0xe7UT3MC+eD70vjfJS5mPkXHjk8tqz9XJ6qhRn4KfLpF0w9pfhxxbt6+sJ7djSKc1uCT4NIdfkCd1Rhw8blmsfykHl5KB/8gjEkn4H0k+DIoagwzFO2pgHfYPrlhTTRg32ZPS+vADpTpsNSQR2x1jtHyuoPAp0YPanrAfLzBmbQ3vFu5VesUckHe6Iy5MgxJyU9nJxgncXnKQY+o3qt82y5kO+kh5/wxffrhRQHbK9OD/ybc3RGBx62o+iRTuL3MSLm9zFHrBj0DW1wQaf3hP8kKv/XC4Y4WxFiWHyhTqWIwsnRd6ORbC3jaTc+d3Ek1PgYkUwxQ49YGf0b2nDULt/7exuRLJgZhTpxoxvqW3bSwOTIT5jvOmF/tYUsSF31V7fxuYTr7nqsE6kuY/IxogHxqXBs9PyGNrhgP4ZkCFz/eBoZhWaYl8tVwzmMp4Q6x/ke+f1Y37i+M1PdPa+2l5Jwkla+zBvcEV5rojTI4ODbl97qKAvjUjVPbnWOg9T+H6autpHYS318DZarD+z+5X1dbVd1Lg5Z4zM4+OCt+IY+KBW51TlGXvt/6LnsaCTl0pClTfx/l2ej6mlHsSB1SPkH1WNZF53NqujcvKIXX+RWKgOs80M1wMjrypNdHS7T3ZDowHrKNbnHutNuC59ZAs595UrnU7eB23N4H7su4r23oIjkNVUjB4mdyrRLg2paCLlXbLrOyaU+Icua5ET12XN8kbkVUTt1LbEtwLcNLYxR9DDvx5azpQNsHedt7ggobS54HyjT0igqFLVtb/AxIrlqO6cRAabvc+9otZc2uVLNb2vDw7rWdjzTwXmbJwL7vcG64oAbyWozHnLGiP5g3WRoHyP8Qn2oEVG9yw0dKNPeEmm8Txv65doJbgNpl3Nb5+17lfrO/xVUbfaMKOWmLKbLe0bkytGpMJVKpTuU3yOWuw25lpD99zC820Ykl/akRG6ft5G/T+Gi5L7/CeVr4ZxtoCBR28KCj7A1qKnkpJaWpXRuc8ZouSIgJ9/wC0M528Af2KlxadtH4OSn7XUoRX+iFmTaJnNt5t9nBkqqzX5nGFB+c2XONjQw70cNyBMOYKYKlD4/5fmogHLTIn/nzGeCe0D59KpGKH0rAVywzmr7Km4hcMfvuBylvb2iKIqiKIqiKIqiKIqiKIqiKL+Lv3chUd0uCDw9AAAAAElFTkSuQmCC" alt="exp(x) = pFq([],[],x)" style="width: 104.5px; height: 21px;" width="104.5" height="21"></span></div><div style="block-size: 39px; 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 19.5px; text-align: left; transform-origin: 384px 19.5px; 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: 13.6px 7.8px; transform-origin: 13.6px 7.8px; unicode-bidi: normal; "><span style="">       </span></span><span style="vertical-align:-16px"><img src="data:image/png;base64,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" alt="cos(x0 = pFq([],1/2,-x^2/4)" style="width: 160.5px; height: 39px;" width="160.5" height="39"></span></div><div style="block-size: 39px; 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 19.5px; text-align: left; transform-origin: 384px 19.5px; 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: 13.6px 7.8px; transform-origin: 13.6px 7.8px; unicode-bidi: normal; "><span style="">       </span></span><span style="vertical-align:-16px"><img src="data:image/png;base64,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" alt="besselj(0,x) = pFq([],1,-x^2/4)" style="width: 149px; height: 39px;" width="149" height="39"></span></div><div style="block-size: 42.45px; 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 21.2333px; text-align: left; transform-origin: 384px 21.2333px; 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: 379.9px 7.8px; transform-origin: 379.9px 7.8px; unicode-bidi: normal; "><span style="">where the dash means that the list of parameters is empty. The generalized hypergeometric function can be computed with</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 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; "><span style=""> </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: 34.65px 7.8px; transform-origin: 34.65px 7.8px; unicode-bidi: normal; "><span style="font-family: Menlo, Monaco, Consolas, &quot;Courier New&quot;, monospace; perspective-origin: 34.65px 8.25px; transform-origin: 34.65px 8.25px; ">hypergeom</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: 252.3px 7.8px; transform-origin: 252.3px 7.8px; unicode-bidi: normal; "><span style=""> from the Symbolic Math Toolbox, but it is not available in Cody or basic MATLAB.</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: 213.05px 7.8px; transform-origin: 213.05px 7.8px; unicode-bidi: normal; "><span style="">Write a function to evaluate the generalized hypergeometric function.</span></span></div></div></div>

Solve

Solution Stats

15 Solutions
5 Solvers

Last Solution submitted on Oct 26, 2022

Last 200 Solutions

Solution Comments

Show comments

Problem Recent Solvers5

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 46043. Evaluate the generalized hypergeometric function

Solution Stats

Last 200 Solutions

Solution Comments

Problem Recent Solvers5

Suggested Problems

More from this Author206

Problem Tags

Community Treasure Hunt

Problem 46043. Evaluate the generalized hypergeometric function

Solution Stats

Last 200 Solutions

Solution Comments

Problem Recent Solvers5

Suggested Problems

More from this Author206

Problem Tags

Community Treasure Hunt

Players