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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=-19/4, b>=a > For fixed z and a=-19/4, b=15/4





http://functions.wolfram.com/07.23.03.a9pb.01









  


  








Input Form





Hypergeometric2F1[-(19/4), 15/4, 3, z] == (1/(4542615 Pi Sqrt[1 + Sqrt[z]] z^2)) (64 (4 (-95 - 95 Sqrt[z] - 1140 z - 1140 z^(3/2) + 30957 z^2 + 30957 z^(5/2) - 117654 z^3 - 117654 z^(7/2) + 178380 z^4 + 178380 z^(9/2) - 121680 z^5 - 121680 z^(11/2) + 31200 z^6 + 31200 z^(13/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - (-380 - 4465 z - 16962 z^2 + 368247 z^3 - 1202520 z^4 + 1642320 z^5 - 1035840 z^6 + 249600 z^7) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))








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