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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=-1/4





http://functions.wolfram.com/07.23.03.a9c6.01









  


  










Input Form





Hypergeometric2F1[-(19/4), -(1/4), 6, z] == (1/(25488471943935 Pi z^5)) (16384 Sqrt[1 + Sqrt[z]] ((428032 - 5397216 z + 32965779 z^2 - 136680775 z^3 + 517506990 z^4 + 3559913994 z^5 + 70835583 z^6 - 15241707 z^7 + 2386800 z^8 - 185640 z^9) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-428032 + 428032 Sqrt[z] + 5076192 z - 5076192 z^(3/2) - 29208795 z^2 + 29208795 z^(5/2) + 115350235 z^3 - 115350235 z^(7/2) - 434203770 z^4 + 434203770 z^(9/2) - 761838714 z^5 + 761838714 z^(11/2) + 121635969 z^6 - 121635969 z^(13/2) - 27139905 z^7 + 27139905 z^(15/2) + 4495140 z^8 - 4495140 z^(17/2) - 371280 z^9 + 371280 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