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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=1/4, b>=a > For fixed z and a=1/4, b=1/4





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









  


  










Input Form





Hypergeometric2F1[1/4, 1/4, 9/2, z] == (1/(22815 Pi^(3/2) z^(7/2))) (112 (-8 (-30 + 123 z - 200 z^2 + 203 z^3) EllipticE[(1/2) (1 - Sqrt[z])] + 8 (-30 + 123 z - 200 z^2 + 203 z^3) EllipticE[(1/2) (1 + Sqrt[z])] + (-120 - 60 Sqrt[z] + 492 z + 241 z^(3/2) - 800 z^2 - 382 z^(5/2) + 812 z^3 + 585 z^(7/2)) EllipticK[(1/2) (1 - Sqrt[z])] + (120 - 60 Sqrt[z] - 492 z + 241 z^(3/2) + 800 z^2 - 382 z^(5/2) - 812 z^3 + 585 z^(7/2)) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^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