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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 4 and fixed z > For fixed z and a=-9/2, b>=a > For fixed z and a=-9/2, b=7/4





http://functions.wolfram.com/07.23.03.aa2r.01









  


  








Input Form





Hypergeometric2F1[-(9/2), 7/4, 4, z] == (1/(225225 Pi Sqrt[1 + Sqrt[1 - z]] z^3)) (Sqrt[2] (2 (-21504 + 98112 z - 70560 z^2 + 341120 z^3 - 496640 z^4 + 371748 z^5 - 144534 z^6 + 23205 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (-21504 + 98112 z - 70560 z^2 + 341120 z^3 - 496640 z^4 + 371748 z^5 - 144534 z^6 + 23205 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (21504 - 98112 z + 70560 z^2 - 341120 z^3 + 496640 z^4 - 371748 z^5 + 144534 z^6 - 23205 z^7) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (21504 - 98112 z + 70560 z^2 - 341120 z^3 + 496640 z^4 - 371748 z^5 + 144534 z^6 - 23205 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (21504 - 98112 z + 70560 z^2 - 341120 z^3 + 496640 z^4 - 371748 z^5 + 144534 z^6 - 23205 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (21504 - 87360 z + 30240 z^2 + 112480 z^3 - 278720 z^4 + 270972 z^5 - 125970 z^6 + 23205 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))








Standard Form





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MathML Form







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Rule Form





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





2007-05-02