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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=1/8, b>=a > For fixed z and a=1/8, b=37/8





http://functions.wolfram.com/07.23.03.by0s.01









  


  








Input Form





Hypergeometric2F1[1/8, 37/8, 5, z] == (65536 2^(1/4) (-16 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (384 + 436 z + 545 z^2 + 840 z^3) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 8 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (384 + 436 z + 545 z^2 + 840 z^3) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 8 Sqrt[1 - z] (384 + 436 z + 545 z^2 + 840 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (3072 + 2336 z + 2737 z^2 + 4560 z^3 + 26880 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (987843675 Pi (1 + Sqrt[1 - z])^(1/4) z^4)








Standard Form





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MathML Form







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</cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <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