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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 8 and fixed z and a>0 > For fixed z and a=37/8, b>=a > For fixed z and a=37/8, b=39/8





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









  


  










Input Form





Hypergeometric2F1[37/8, 39/8, 1, z] == (1/(9408035 Pi (-1 + z)^9)) (2^(3/4) (1 + Sqrt[1 - z])^(1/4) (64 (-1 + z) (378841 + 2882701 z + 2927323 z^2 + 400575 z^3) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 32 (-1 + z) (378841 + 2882701 z + 2927323 z^2 + 400575 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (1/z) (5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-1 + z) (1881607 + 27100180 z + 54488090 z^2 + 20966260 z^3 + 994903 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]) + (1/z) (Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-9408035 - 129439444 z - 226317234 z^2 - 57994132 z^3 + 1434685 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])])))










Standard Form





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MathML Form







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<power /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </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> </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