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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=5/4





http://functions.wolfram.com/07.23.03.aa2b.01









  


  








Input Form





Hypergeometric2F1[-(9/2), 5/4, 4, z] == (1/(45045 Pi Sqrt[1 + Sqrt[1 - z]] z^3)) (Sqrt[2] (2 (1 - z)^(1/4) (-3072 + 19008 z - 42336 z^2 + 115264 z^3 - 132096 z^4 + 85140 z^5 - 29722 z^6 + 4389 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (-3072 + 19008 z - 42336 z^2 + 115264 z^3 - 132096 z^4 + 85140 z^5 - 29722 z^6 + 4389 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (3072 - 19008 z + 42336 z^2 - 115264 z^3 + 132096 z^4 - 85140 z^5 + 29722 z^6 - 4389 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (3072 - 19008 z + 42336 z^2 - 115264 z^3 + 132096 z^4 - 85140 z^5 + 29722 z^6 - 4389 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (3072 - 19008 z + 42336 z^2 - 115264 z^3 + 132096 z^4 - 85140 z^5 + 29722 z^6 - 4389 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (3072 - 20544 z + 51552 z^2 - 44704 z^3 + 48608 z^4 - 30132 z^5 + 10186 z^6 - 1463 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 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