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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=-3/4





http://functions.wolfram.com/07.23.03.aeu1.01









  


  








Input Form





Hypergeometric2F1[-(7/4), -(3/4), 5, -z] == (4096 Sqrt[2] ((-Sqrt[1 + z]) (384 + 3280 z + 13767 z^2 + 46125 z^3 - 98891 z^4 + 3135 z^5) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (384 + 3664 z + 17047 z^2 + 59892 z^3 - 52766 z^4 - 95756 z^5 + 3135 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + Sqrt[1 + z] (384 + 3280 z + 13767 z^2 + 46125 z^3 - 98891 z^4 + 3135 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 8 (-48 - 446 z - 2025 z^2 - 7029 z^3 - 24047 z^4 + 15675 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (527448075 Pi z^4 Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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<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='rational'> 1 <sep /> 2 </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