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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=-3/8, b>=a > For fixed z and a=-3/8, b=39/8





http://functions.wolfram.com/07.23.03.bw16.01









  


  








Input Form





Hypergeometric2F1[-(3/8), 39/8, 4, z] == (1/(140821065 Pi z^3)) (1024 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (-896 - 2877 z - 9828 z^2 + 53040 z^3) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 10 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (56 + 189 z - 13104 z^2 + 10608 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (1/Sqrt[1 - z]) (3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-112 - 329 z - 46956 z^2 + 53040 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]) - 2 (-896 - 2877 z - 9828 z^2 + 53040 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))








Standard Form





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MathML Form







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<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