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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=11/4





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









  


  








Input Form





Hypergeometric2F1[7/4, 11/4, 11/2, z] == (1/(77 Pi^(3/2) z^(9/2))) (40 (2 Sqrt[z] (40 - 40 z + 3 z^2) EllipticE[(1/2) (1 - Sqrt[z])] + 2 Sqrt[z] (40 - 40 z + 3 z^2) EllipticE[(1/2) (1 + Sqrt[z])] - (-80 + 40 Sqrt[z] + 140 z - 40 z^(3/2) - 57 z^2 + 3 z^(5/2)) EllipticK[(1/2) (1 - Sqrt[z])] - (80 + 40 Sqrt[z] - 140 z - 40 z^(3/2) + 57 z^2 + 3 z^(5/2)) EllipticK[(1/2) (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