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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=11/8, b>=a > For fixed z and a=11/8, b=41/8





http://functions.wolfram.com/07.23.03.c3sf.01









  


  










Input Form





Hypergeometric2F1[11/8, 41/8, 3, z] == (256 2^(1/4) (8 Sqrt[1 - z] (102 - 153 z + 1452 z^2 - 1463 z^3 + 462 z^4) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + 4 Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (102 - 153 z + 1452 z^2 - 1463 z^3 + 462 z^4) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (-1 + z) (-408 + 459 z - 759 z^2 + 308 z^3) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 4 Sqrt[1 - z] (102 - 153 z + 1452 z^2 - 1463 z^3 + 462 z^4) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (631125 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] (-1 + z)^4 z^2)










Standard Form





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MathML Form







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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