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variants of this functions
Hypergeometric2F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > For rational parameters with denominators 4 and fixed z > For fixed z and a=-11/2, b>=a > For fixed z and a=-11/2, b=15/4





http://functions.wolfram.com/07.23.03.a82r.01









  


  








Input Form





Hypergeometric2F1[-(11/2), 15/4, 6, z] == (8 Sqrt[2] (-2 (393216 - 1241088 z + 372480 z^2 + 545280 z^3 + 1841280 z^4 - 23568832 z^5 + 58520336 z^6 - 70307920 z^7 + 46476300 z^8 - 16342950 z^9 + 2403375 z^10) EllipticE[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (393216 - 1241088 z + 372480 z^2 + 545280 z^3 + 1841280 z^4 - 23568832 z^5 + 58520336 z^6 - 70307920 z^7 + 46476300 z^8 - 16342950 z^9 + 2403375 z^10) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (393216 - 1241088 z + 372480 z^2 + 545280 z^3 + 1841280 z^4 - 23568832 z^5 + 58520336 z^6 - 70307920 z^7 + 46476300 z^8 - 16342950 z^9 + 2403375 z^10) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (393216 - 1241088 z + 372480 z^2 + 545280 z^3 + 1841280 z^4 - 23568832 z^5 + 58520336 z^6 - 70307920 z^7 + 46476300 z^8 - 16342950 z^9 + 2403375 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (393216 - 1241088 z + 372480 z^2 + 545280 z^3 + 1841280 z^4 - 23568832 z^5 + 58520336 z^6 - 70307920 z^7 + 46476300 z^8 - 16342950 z^9 + 2403375 z^10) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (-393216 + 1044480 z + 88320 z^2 - 368640 z^3 - 1948800 z^4 - 2881088 z^5 + 24076080 z^6 - 42237520 z^7 + 34940100 z^8 - 14420250 z^9 + 2403375 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (101846745 Pi Sqrt[1 + Sqrt[1 - z]] z^5)








Standard Form





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MathML Form







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<mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2403375 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 14420250 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 34940100 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 42237520 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 24076080 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2881088 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1948800 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 368640 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 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<apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1044480 </cn> <ci> z </ci> </apply> <cn type='integer'> -393216 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 101846745 </cn> <pi /> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02