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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.ccl6.01









  


  








Input Form





Hypergeometric2F1[35/8, 39/8, 5, z] == (65536 2^(1/4) (8 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-256 + 1032 z - 1593 z^2 + 1207 z^3) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (1024 (1 + Sqrt[1 - z] + Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) - 96 (47 + 43 Sqrt[1 - z] + 43 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z + (7815 + 6372 Sqrt[1 - z] + 6372 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^2 - 2 (3425 + 2414 Sqrt[1 - z] + 2414 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^3 + 5643 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)^(17/4) z^4)








Standard Form





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MathML Form







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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'> 17 <sep /> 4 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 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