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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=-9/4





http://functions.wolfram.com/07.23.03.a970.01









  


  










Input Form





Hypergeometric2F1[-(19/4), -(9/4), 6, z] == (1/(410647603541175 Pi z^5)) (16384 Sqrt[1 + Sqrt[z]] ((428032 - 7483872 z + 67569491 z^2 - 455344120 z^3 + 3271933665 z^4 + 72101451786 z^5 + 92615701269 z^6 + 21355944948 z^7 + 29321175 z^8 - 961350 z^9) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-428032 + 428032 Sqrt[z] + 7162848 z - 7162848 z^(3/2) - 62247515 z^2 + 62247515 z^(5/2) + 409479070 z^3 - 409479070 z^(7/2) - 2971813845 z^4 + 2971813845 z^(9/2) - 24157025256 z^5 + 24157025256 z^(11/2) - 18641760501 z^6 + 18641760501 z^(13/2) - 1883284650 z^7 + 1883284650 z^(15/2) + 57200325 z^8 - 57200325 z^(17/2) - 1922700 z^9 + 1922700 z^(19/2)) 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