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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=-17/4, b>=a > For fixed z and a=-17/4, b=-5/4





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









  


  








Input Form





Hypergeometric2F1[-(17/4), -(5/4), 4, -z] == (256 Sqrt[2] ((-32 - 491 z - 4977 z^2 + 172890 z^3 - 172890 z^4 + 4977 z^5 + 491 z^6 + 32 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + Sqrt[1 + z] (-32 - 491 z - 4977 z^2 + 172890 z^3 - 172890 z^4 + 4977 z^5 + 491 z^6 + 32 z^7) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - Sqrt[1 + z] (-32 - 483 z - 4860 z^2 + 95190 z^3 - 77700 z^4 + 117 z^5 + 8 z^6) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - (-32 - 491 z - 4977 z^2 + 172890 z^3 - 172890 z^4 + 4977 z^5 + 491 z^6 + 32 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (10094175 Pi z^3 Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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</ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 491 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -32 </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