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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=7/4





http://functions.wolfram.com/07.23.03.a80x.01









  


  








Input Form





Hypergeometric2F1[-(11/2), 7/4, 6, z] == (8 Sqrt[2] (-2 (1441792 - 12120064 z + 42366720 z^2 - 72787968 z^3 + 28828800 z^4 - 98215104 z^5 + 120952208 z^6 - 87392240 z^7 + 38647596 z^8 - 9739470 z^9 + 1077375 z^10) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (1441792 - 12120064 z + 42366720 z^2 - 72787968 z^3 + 28828800 z^4 - 98215104 z^5 + 120952208 z^6 - 87392240 z^7 + 38647596 z^8 - 9739470 z^9 + 1077375 z^10) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1441792 - 12120064 z + 42366720 z^2 - 72787968 z^3 + 28828800 z^4 - 98215104 z^5 + 120952208 z^6 - 87392240 z^7 + 38647596 z^8 - 9739470 z^9 + 1077375 z^10) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (1441792 - 12120064 z + 42366720 z^2 - 72787968 z^3 + 28828800 z^4 - 98215104 z^5 + 120952208 z^6 - 87392240 z^7 + 38647596 z^8 - 9739470 z^9 + 1077375 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (1441792 - 12120064 z + 42366720 z^2 - 72787968 z^3 + 28828800 z^4 - 98215104 z^5 + 120952208 z^6 - 87392240 z^7 + 38647596 z^8 - 9739470 z^9 + 1077375 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (-1441792 + 11399168 z - 36892416 z^2 + 56010240 z^3 - 5765760 z^4 - 40163136 z^5 + 70857904 z^6 - 62102768 z^7 + 31545540 z^8 - 8877570 z^9 + 1077375 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (567431865 Pi Sqrt[1 + Sqrt[1 - z]] z^5)








Standard Form





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MathML Form







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<mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 11 <sep /> 2 </cn> </apply> <cn type='rational'> 7 <sep /> 4 </cn> </list> <list> <cn type='integer'> 6 </cn> </list> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <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> <apply> <plus /> <apply> <times /> <cn type='integer'> 1077375 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn 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<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'> 567431865 </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