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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=13/4, b>=a > For fixed z and a=13/4, b=13/4





http://functions.wolfram.com/07.23.03.am7w.01









  


  








Input Form





Hypergeometric2F1[13/4, 13/4, 1/2, z] == (1/(675 Pi^(3/2))) ((-((8 Sqrt[z] (2139 + 6474 z + 1627 z^2) EllipticE[(1/2) (1 - Sqrt[z])])/ (-1 + z)^6) + (8 Sqrt[z] (2139 + 6474 z + 1627 z^2) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^6 + ((675 + 7881 Sqrt[z] + 6522 z + 19374 z^(3/2) + 3043 z^2 + 3465 z^(5/2)) EllipticK[(1/2) (1 - Sqrt[z])])/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^5) + ((-675 + 7881 Sqrt[z] - 6522 z + 19374 z^(3/2) - 3043 z^2 + 3465 z^(5/2)) EllipticK[(1/2) (1 + Sqrt[z])])/((-1 + Sqrt[z])^5 (1 + Sqrt[z])^6)) 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