{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":59541,"title":"Compute the polylogarithm for real arguments","description":"The polylogarithm  appears in quantum statistics and quantum electrodynamics, and for special cases of  and , it connects to the logarithm, ratios of polynomials, the zeta function, the Dirichlet eta function, and other functions. \r\nWrite a function to compute the polylogarithm  for real arguments. ","description_html":"\u003cdiv 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; \"\u003e\u003cdiv style=\"block-size: 74px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 37px; transform-origin: 407px 37px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 43px; 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 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan 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: 57.575px 8px; transform-origin: 57.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe polylogarithm \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"20\" alt=\"Li_n(z)\" style=\"width: 39px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan 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: 267.225px 8px; transform-origin: 267.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e appears in quantum statistics and quantum electrodynamics, and for special cases of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan 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; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ez\u003c/span\u003e\u003cspan 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: 9.325px 8px; transform-origin: 9.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, it connects to the logarithm, ratios of polynomials, the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45988\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ezeta\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan 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; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45997\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003efunction\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan 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: 146.242px 8px; transform-origin: 146.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the Dirichlet eta function, and other functions. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv 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; \"\u003e\u003cspan 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: 142.233px 8px; transform-origin: 142.233px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the polylogarithm \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"20\" alt=\"Li_n(z)\" style=\"width: 39px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan 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: 62.6167px 8px; transform-origin: 62.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for real arguments. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = polylogarithm(n,z)\r\n  y = sum(z^k/k^n);\r\nend","test_suite":"%%\r\nn = 2:2:16;\r\nz = 1;\r\ny = arrayfun(@(m) polylogarithm(m,z),n);\r\ny_correct = pi.^n.*[1/6 1/90 1/945 1/9450 1/93555 691/638512875 2/18243225 3617/325641566250];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 3;\r\nz = 1;\r\ny = polylogarithm(n,z);\r\ny_correct = 1.202056903159594;\r\nassert(abs(y-y_correct)\u003c1e-12)\r\n\r\n%%\r\nn = 0;\r\nz = 1./(10:-1:2);\r\ny = arrayfun(@(s) polylogarithm(n,s),z);\r\ny_correct = 1./(9:-1:1);\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 1;\r\nz = [-2 -3/2 -1 -1/2 0 1/10 1/7 1/5 1/3 1/2];\r\ny = arrayfun(@(s) polylogarithm(n,s),z);\r\ny_correct = [-1.098612288668110 -0.916290731874155 -0.693147180559945 -0.405465108108164 0 0.105360515657826 0.154150679827258 0.223143551314210 0.405465108108164 0.693147180559945];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = -1;\r\nz = [-2 -3/2 -1 -1/2 1/7 1/5 1/2];\r\ny = arrayfun(@(s) polylogarithm(n,s),z);\r\ny_correct = [-2/9 -6/25 -1/4 -2/9 7/36 5/16 2];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = -2;\r\nz = [-2 -3/2 -1 -1/2 0 1/17 1/13 1/11 1/5];\r\ny = arrayfun(@(s) polylogarithm(n,s),z);\r\ny_correct = [2/27 6/125 0 -2/27 0 153/2048 91/864 33/250 15/32];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 1:3;\r\nz = 1/2;\r\ny = arrayfun(@(m) polylogarithm(m,z),n);\r\nzeta3 = 1.202056903159594;\r\ny_correct = [log(2) (pi^2-6*log(2)^2)/12 (4*log(2)^3-2*pi^2*log(2)+21*zeta3)/24];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 2;\r\nz = -1;\r\ny = polylogarithm(n,z);\r\ny_correct = -pi^2/12;\r\nassert(abs(y-y_correct)\u003c1e-12)\r\n\r\n%%\r\nn = -1/pi;\r\nz = exp(-1);\r\ny = polylogarithm(n,z);\r\ny_correct = 0.6541056465726233;\r\nassert(abs(y-y_correct)\u003c1e-12)\r\n\r\n%%\r\nn = 4;\r\nz = 1/2;\r\ny = polylogarithm(n,z);\r\ny_correct = 0.5174790616738994;\r\nassert(abs(y-y_correct)\u003c1e-12)\r\n\r\n%%\r\nn = 1/2;\r\nz = 1/2;\r\ny = polylogarithm(n,z);\r\ny_correct = 0.8061267230428522;\r\nassert(abs(y-y_correct)\u003c1e-12)\r\n\r\n%%\r\nn = -3/2;\r\nz = -1./2.^(1:4);\r\ny = arrayfun(@(s) polylogarithm(n,s),z);\r\ny_correct = [-0.1516441361365191 -0.1313580923579523 -0.0892942267818043 -0.05260782861980105];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 5*randn(1,randi(10));\r\nz = 0;\r\ny = arrayfun(@(m) polylogarithm(m,z),n);\r\ny_correct = zeros(size(n));\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nfiletext = fileread('polylogarithm.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-01-07T03:51:00.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-01-06T17:30:34.000Z","updated_at":"2025-02-27T16:14:20.000Z","published_at":"2024-01-06T17:31:22.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe polylogarithm \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Li_n(z)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e{\\\\rm Li}_n(z)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e appears in quantum statistics and quantum electrodynamics, and for special cases of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, it connects to the logarithm, ratios of polynomials, the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45988\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ezeta\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45997\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efunction\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, the Dirichlet eta function, and other functions. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the polylogarithm \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Li_n(z)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e{\\\\rm Li}_n(z)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for real arguments. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":59541,"title":"Compute the polylogarithm for real arguments","description":"The polylogarithm  appears in quantum statistics and quantum electrodynamics, and for special cases of  and , it connects to the logarithm, ratios of polynomials, the zeta function, the Dirichlet eta function, and other functions. \r\nWrite a function to compute the polylogarithm  for real arguments. ","description_html":"\u003cdiv 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; \"\u003e\u003cdiv style=\"block-size: 74px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 37px; transform-origin: 407px 37px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 43px; 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 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan 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: 57.575px 8px; transform-origin: 57.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe polylogarithm \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"20\" alt=\"Li_n(z)\" style=\"width: 39px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan 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: 267.225px 8px; transform-origin: 267.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e appears in quantum statistics and quantum electrodynamics, and for special cases of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan 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; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ez\u003c/span\u003e\u003cspan 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: 9.325px 8px; transform-origin: 9.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, it connects to the logarithm, ratios of polynomials, the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45988\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ezeta\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan 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; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45997\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003efunction\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan 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: 146.242px 8px; transform-origin: 146.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the Dirichlet eta function, and other functions. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv 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; \"\u003e\u003cspan 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: 142.233px 8px; transform-origin: 142.233px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the polylogarithm \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"20\" alt=\"Li_n(z)\" style=\"width: 39px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan 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: 62.6167px 8px; transform-origin: 62.6167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for real arguments. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = polylogarithm(n,z)\r\n  y = sum(z^k/k^n);\r\nend","test_suite":"%%\r\nn = 2:2:16;\r\nz = 1;\r\ny = arrayfun(@(m) polylogarithm(m,z),n);\r\ny_correct = pi.^n.*[1/6 1/90 1/945 1/9450 1/93555 691/638512875 2/18243225 3617/325641566250];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 3;\r\nz = 1;\r\ny = polylogarithm(n,z);\r\ny_correct = 1.202056903159594;\r\nassert(abs(y-y_correct)\u003c1e-12)\r\n\r\n%%\r\nn = 0;\r\nz = 1./(10:-1:2);\r\ny = arrayfun(@(s) polylogarithm(n,s),z);\r\ny_correct = 1./(9:-1:1);\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 1;\r\nz = [-2 -3/2 -1 -1/2 0 1/10 1/7 1/5 1/3 1/2];\r\ny = arrayfun(@(s) polylogarithm(n,s),z);\r\ny_correct = [-1.098612288668110 -0.916290731874155 -0.693147180559945 -0.405465108108164 0 0.105360515657826 0.154150679827258 0.223143551314210 0.405465108108164 0.693147180559945];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = -1;\r\nz = [-2 -3/2 -1 -1/2 1/7 1/5 1/2];\r\ny = arrayfun(@(s) polylogarithm(n,s),z);\r\ny_correct = [-2/9 -6/25 -1/4 -2/9 7/36 5/16 2];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = -2;\r\nz = [-2 -3/2 -1 -1/2 0 1/17 1/13 1/11 1/5];\r\ny = arrayfun(@(s) polylogarithm(n,s),z);\r\ny_correct = [2/27 6/125 0 -2/27 0 153/2048 91/864 33/250 15/32];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 1:3;\r\nz = 1/2;\r\ny = arrayfun(@(m) polylogarithm(m,z),n);\r\nzeta3 = 1.202056903159594;\r\ny_correct = [log(2) (pi^2-6*log(2)^2)/12 (4*log(2)^3-2*pi^2*log(2)+21*zeta3)/24];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 2;\r\nz = -1;\r\ny = polylogarithm(n,z);\r\ny_correct = -pi^2/12;\r\nassert(abs(y-y_correct)\u003c1e-12)\r\n\r\n%%\r\nn = -1/pi;\r\nz = exp(-1);\r\ny = polylogarithm(n,z);\r\ny_correct = 0.6541056465726233;\r\nassert(abs(y-y_correct)\u003c1e-12)\r\n\r\n%%\r\nn = 4;\r\nz = 1/2;\r\ny = polylogarithm(n,z);\r\ny_correct = 0.5174790616738994;\r\nassert(abs(y-y_correct)\u003c1e-12)\r\n\r\n%%\r\nn = 1/2;\r\nz = 1/2;\r\ny = polylogarithm(n,z);\r\ny_correct = 0.8061267230428522;\r\nassert(abs(y-y_correct)\u003c1e-12)\r\n\r\n%%\r\nn = -3/2;\r\nz = -1./2.^(1:4);\r\ny = arrayfun(@(s) polylogarithm(n,s),z);\r\ny_correct = [-0.1516441361365191 -0.1313580923579523 -0.0892942267818043 -0.05260782861980105];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 5*randn(1,randi(10));\r\nz = 0;\r\ny = arrayfun(@(m) polylogarithm(m,z),n);\r\ny_correct = zeros(size(n));\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nfiletext = fileread('polylogarithm.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-01-07T03:51:00.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-01-06T17:30:34.000Z","updated_at":"2025-02-27T16:14:20.000Z","published_at":"2024-01-06T17:31:22.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe polylogarithm \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Li_n(z)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e{\\\\rm Li}_n(z)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e appears in quantum statistics and quantum electrodynamics, and for special cases of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, it connects to the logarithm, ratios of polynomials, the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45988\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ezeta\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45997\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efunction\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, the Dirichlet eta function, and other functions. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the polylogarithm \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Li_n(z)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e{\\\\rm Li}_n(z)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for real arguments. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"term":"tag:\"gamma\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"gamma\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"gamma\"","","\"","gamma","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007f46044c0828\u003e":null,"#\u003cMathWorks::Search::Field:0x00007f46044c06e8\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007f46044efdd0\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007f46044c0aa8\u003e":1,"#\u003cMathWorks::Search::Field:0x00007f46044c0a08\u003e":50,"#\u003cMathWorks::Search::Field:0x00007f46044c0968\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007f46044c08c8\u003e":"tag:\"gamma\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007f46044c08c8\u003e":"tag:\"gamma\""},"queried_facets":{}},"query_backend":{"connection":{"configuration":{"index_url":"http://index-op-v2/solr/","query_url":"http://search-op-v2/solr/","direct_access_index_urls":["http://index-op-v2/solr/"],"direct_access_query_urls":["http://search-op-v2/solr/"],"timeout":10,"vhost":"search","exchange":"search.topic","heartbeat":30,"pre_index_mode":false,"host":"rabbitmq-eks","port":5672,"username":"search","password":"J3bGPZzQ7asjJcCk","virtual_host":"search","indexer":"amqp","http_logging":"true","core":"cody"},"query_connection":{"uri":"http://search-op-v2/solr/cody/","proxy":null,"connection":{"parallel_manager":null,"headers":{"User-Agent":"Faraday v1.0.1"},"params":{},"options":{"params_encoder":"Faraday::FlatParamsEncoder","proxy":null,"bind":null,"timeout":null,"open_timeout":null,"read_timeout":null,"write_timeout":null,"boundary":null,"oauth":null,"context":null,"on_data":null},"ssl":{"verify":true,"ca_file":null,"ca_path":null,"verify_mode":null,"cert_store":null,"client_cert":null,"client_key":null,"certificate":null,"private_key":null,"verify_depth":null,"version":null,"min_version":null,"max_version":null},"default_parallel_manager":null,"builder":{"adapter":{"name":"Faraday::Adapter::NetHttp","args":[],"block":null},"handlers":[{"name":"Faraday::Response::RaiseError","args":[],"block":null}],"app":{"app":{"ssl_cert_store":{"verify_callback":null,"error":null,"error_string":null,"chain":null,"time":null},"app":{},"connection_options":{},"config_block":null}}},"url_prefix":"http://search-op-v2/solr/cody/","manual_proxy":false,"proxy":null},"update_format":"RSolr::JSON::Generator","update_path":"update","options":{"url":"http://search-op-v2/solr/cody"}}},"query":{"params":{"per_page":50,"term":"tag:\"gamma\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"gamma\"","","\"","gamma","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007f46044c0828\u003e":null,"#\u003cMathWorks::Search::Field:0x00007f46044c06e8\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007f46044efdd0\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007f46044c0aa8\u003e":1,"#\u003cMathWorks::Search::Field:0x00007f46044c0a08\u003e":50,"#\u003cMathWorks::Search::Field:0x00007f46044c0968\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007f46044c08c8\u003e":"tag:\"gamma\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007f46044c08c8\u003e":"tag:\"gamma\""},"queried_facets":{}},"options":{"fields":["id","difficulty_rating"]},"join":" "},"results":[{"id":59541,"difficulty_rating":"hard"}]}}