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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=19/8, b>=a > For fixed z and a=19/8, b=39/8





http://functions.wolfram.com/07.23.03.c7i2.01









  


  










Input Form





Hypergeometric2F1[19/8, 39/8, 1, z] == (2 2^(1/4) (-4 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-97381 - 267728 z - 6897 z^2 + 726 z^3) EllipticE[ 1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + 2 Sqrt[1 - z] (-97381 - 267728 z - 6897 z^2 + 726 z^3) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + 2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-97381 - 267728 z - 6897 z^2 + 726 z^3) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (79743 + 978731 z + 478797 z^2 - 57959 z^3 + 5808 z^4) EllipticK[ 1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (274505 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(25/4))










Standard Form





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MathML Form







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</apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02