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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=-9/4, b>=a > For fixed z and a=-9/4, b=3/2





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









  


  










Input Form





Hypergeometric2F1[-(9/4), 3/2, 5, z] == (512 Sqrt[2] (2 (576 - 2928 z + 5565 z^2 - 3600 z^3 + 8500 z^4 - 4648 z^5 + 924 z^6) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (576 - 2928 z + 5565 z^2 - 3600 z^3 + 8500 z^4 - 4648 z^5 + 924 z^6) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (-576 + 2640 z - 4335 z^2 + 1800 z^3 - 1300 z^4 + 308 z^5) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (576 - 2928 z + 5565 z^2 - 3600 z^3 + 8500 z^4 - 4648 z^5 + 924 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (576 - 2928 z + 5565 z^2 - 3600 z^3 + 8500 z^4 - 4648 z^5 + 924 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (576 - 2928 z + 5565 z^2 - 3600 z^3 + 8500 z^4 - 4648 z^5 + 924 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (1740375 Pi Sqrt[1 + Sqrt[1 - z]] z^4)










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