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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.ccku.01









  


  










Input Form





Hypergeometric2F1[35/8, 39/8, 3, z] == (256 2^(1/4) (4 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-1540 + 19635 z + 251766 z^2 + 101419 z^3) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (3080 (1 + Sqrt[1 - z] + Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) - 1155 (35 + 34 Sqrt[1 - z] + 34 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z + (611043 - 503532 Sqrt[1 - z] - 503532 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^2 + (849349 - 202838 Sqrt[1 - z] - 202838 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^3 + 62073 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)^(25/4) z^2)










Standard Form





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MathML Form







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<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'> 25 <sep /> 4 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 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