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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=-7/4, b>=a > For fixed z and a=-7/4, b=13/4





http://functions.wolfram.com/07.23.03.af7z.01









  


  








Input Form





Hypergeometric2F1[-(7/4), 13/4, 5, -z] == (4096 Sqrt[2] (Sqrt[1 + z] (896 + 784 z - 721 z^2 + 1043 z^3 + 4000 z^4 + 2048 z^5) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (896 + 1680 z + 63 z^2 + 322 z^3 + 5043 z^4 + 6048 z^5 + 2048 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 4 (224 + 364 z - 49 z^2 + 119 z^3 + 286 z^4 + 128 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (896 + 784 z - 721 z^2 + 1043 z^3 + 4000 z^4 + 2048 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (7571025 Pi z^4 Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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<apply> <times /> <cn type='integer'> 721 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 784 </cn> <ci> z </ci> </apply> <cn type='integer'> 896 </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