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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=35/8, b>=a > For fixed z and a=35/8, b=39/8





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









  


  








Input Form





Hypergeometric2F1[35/8, 39/8, 1, z] == (2 2^(1/4) (272 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (827501 + 6693027 z + 7227243 z^2 + 1086229 z^3) EllipticE[ 1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - (-28280929 + 112540136 Sqrt[1 - z] + 112540136 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] + 12 (-80218727 + 75854306 Sqrt[1 - z] + 75854306 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z + 6 (-394287869 + 163817508 Sqrt[1 - z] + 163817508 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^2 + 4 (-229592921 + 36931786 Sqrt[1 - z] + 36931786 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^3 - 31843449 z^4) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (140821065 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(33/4))








Standard Form





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MathML Form







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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 /> 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'> 33 <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