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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=45/8





http://functions.wolfram.com/07.23.03.bx9s.01









  


  








Input Form





Hypergeometric2F1[-(1/8), 45/8, 4, z] == (1024 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (-1 + z) (1664 + 5239 z + 19734 z^2 - 447216 z^3 + 421344 z^4) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-1 + z) (208 + 689 z - 70356 z^2 + 70224 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 6 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (104 + 299 z + 61919 z^2 - 133056 z^3 + 70224 z^4) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 2 (-1 + z) (1664 + 5239 z + 19734 z^2 - 447216 z^3 + 421344 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (373484475 Pi (-1 + z)^2 z^3)








Standard Form





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MathML Form







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<apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <cn 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 /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02