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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=-3/4, b>=a > For fixed z and a=-3/4, b=9/4





http://functions.wolfram.com/07.23.03.agq5.01









  


  








Input Form





Hypergeometric2F1[-(3/4), 9/4, 6, -z] == (16384 Sqrt[2] (Sqrt[1 + z] (-6144 - 20832 z - 22633 z^2 - 5082 z^3 + 3927 z^4 + 2464 z^5) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (-6144 - 26976 z - 43465 z^2 - 27715 z^3 - 1155 z^4 + 6391 z^5 + 2464 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-6144 - 25440 z - 37825 z^2 - 20790 z^3 + 1155 z^4 + 616 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-6144 - 20832 z - 22633 z^2 - 5082 z^3 + 3927 z^4 + 2464 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (38864595 Pi z^5 Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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</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