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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=7/4, b>=a > For fixed z and a=7/4, b=19/4





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









  


  










Input Form





Hypergeometric2F1[7/4, 19/4, 11/2, z] == (1/(847 Pi^(3/2) z^(9/2))) (8 ((2 Sqrt[z] (-280 + 120 z + 51 z^2 + 32 z^3) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z) + (2 Sqrt[z] (-280 + 120 z + 51 z^2 + 32 z^3) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z) - ((560 - 840 Sqrt[z] + 180 z - 60 z^(3/2) + 75 z^2 - 24 z^(5/2) + 32 z^3) EllipticK[(1/2) (1 - Sqrt[z])])/(-1 + Sqrt[z]) - ((560 + 840 Sqrt[z] + 180 z + 60 z^(3/2) + 75 z^2 + 24 z^(5/2) + 32 z^3) EllipticK[(1/2) (1 + Sqrt[z])])/(1 + Sqrt[z])) Gamma[1/4]^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