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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=-25/8, b>=a > For fixed z and a=-25/8, b=27/8





http://functions.wolfram.com/07.23.03.bj9s.01









  


  








Input Form





Hypergeometric2F1[-(25/8), 27/8, 1, z] == (2 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (1348477 - 12043360 z + 24756480 z^2 - 14192640 z^3) EllipticE[ 1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (-549052 - 1348477 Sqrt[1 - z] - 1348477 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] + 28 (137689 + 430120 Sqrt[1 - z] + 430120 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z - 80640 (85 + 307 Sqrt[1 - z] + 307 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^2 + 3548160 (1 + 4 Sqrt[1 - z] + 4 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^3) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (799425 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(1/4))








Standard Form





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MathML Form







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<sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <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 /> 4 </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