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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=3/4





http://functions.wolfram.com/07.23.03.a9eu.01









  


  










Input Form





Hypergeometric2F1[-(19/4), 3/4, 6, z] == (1/(1213736759235 Pi z^5)) (16384 Sqrt[1 + Sqrt[z]] ((428032 - 4353888 z + 20228483 z^2 - 57561735 z^3 + 119249130 z^4 + 36278034 z^5 - 19284681 z^6 + 7098741 z^7 - 1577940 z^8 + 159120 z^9) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-428032 + 428032 Sqrt[z] + 4032864 z - 4032864 z^(3/2) - 17253995 z^2 + 17253995 z^(5/2) + 45075030 z^3 - 45075030 z^(7/2) - 87297210 z^4 + 87297210 z^(9/2) + 51019176 z^5 - 51019176 z^(11/2) - 29748147 z^6 + 29748147 z^(13/2) + 12033450 z^7 - 12033450 z^(15/2) - 2917200 z^8 + 2917200 z^(17/2) + 318240 z^9 - 318240 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