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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=31/8, b>=a > For fixed z and a=31/8, b=35/8





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









  


  








Input Form





Hypergeometric2F1[31/8, 35/8, 6, z] == (524288 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-32768 + 68736 z - 39843 z^2 + 4025 z^3) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (32768 (1 + Sqrt[1 - z] + Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) - 384 (211 + 179 Sqrt[1 - z] + 179 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z + (62259 + 39843 Sqrt[1 - z] + 39843 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^2 - (13703 + 4025 Sqrt[1 - z] + 4025 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^3) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (40883535 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(9/4) z^5)








Standard Form





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MathML Form







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<times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 9 <sep /> 4 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </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