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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=3/4





http://functions.wolfram.com/07.23.03.aa1u.01









  


  








Input Form





Hypergeometric2F1[-(9/2), 3/4, 3, z] == (2 (-8064 + 64512 z + 101168 z^2 - 101168 z^3 + 63336 z^4 - 22152 z^5 + 3315 z^6) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (-8064 + 64512 z + 101168 z^2 - 101168 z^3 + 63336 z^4 - 22152 z^5 + 3315 z^6) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (8064 - 64512 z - 101168 z^2 + 101168 z^3 - 63336 z^4 + 22152 z^5 - 3315 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (8064 - 64512 z - 101168 z^2 + 101168 z^3 - 63336 z^4 + 22152 z^5 - 3315 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (8064 - 64512 z - 101168 z^2 + 101168 z^3 - 63336 z^4 + 22152 z^5 - 3315 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (8064 - 60480 z + 50032 z^2 - 62816 z^3 + 47736 z^4 - 19500 z^5 + 3315 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])/ (45045 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z^2)








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