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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=-11/4, b>=a > For fixed z and a=-11/4, b=5/4





http://functions.wolfram.com/07.23.03.ad9x.01









  


  








Input Form





Hypergeometric2F1[-(11/4), 5/4, 5, -z] == (4096 Sqrt[2] (2 Sqrt[1 + z] (64 + 360 z + 801 z^2 + 770 z^3 + 801 z^4 + 360 z^5 + 64 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + 2 (64 + 424 z + 1161 z^2 + 1571 z^3 + 1571 z^4 + 1161 z^5 + 424 z^6 + 64 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (128 + 816 z + 2133 z^2 + 2695 z^3 + 447 z^4 + 189 z^5 + 32 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 2 Sqrt[1 + z] (64 + 360 z + 801 z^2 + 770 z^3 + 801 z^4 + 360 z^5 + 64 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (4542615 Pi z^4 Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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<times /> <cn type='integer'> 360 </cn> <ci> z </ci> </apply> <cn type='integer'> 64 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </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> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02