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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=-19/4





http://functions.wolfram.com/07.23.03.a90a.01









  


  










Input Form





Hypergeometric2F1[-(19/4), -(19/4), 9/4, z] == (1/(34359738368 z^(5/4))) (8 (1 - z)^(3/4) z^(1/4) (10701845 + 2762463092 z + 19380532736 z^2 + 28385643520 z^3 + 10063842304 z^4 + 622686208 z^5) - 14630 Sqrt[2] (-1463 + 210672 z + 3511200 z^2 + 10700800 z^3 + 8755200 z^4 + 1867776 z^5 + 65536 z^6) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 14630 Sqrt[2] (-1463 + 210672 z + 3511200 z^2 + 10700800 z^3 + 8755200 z^4 + 1867776 z^5 + 65536 z^6) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 7315 Sqrt[2] (-1463 + 210672 z + 3511200 z^2 + 10700800 z^3 + 8755200 z^4 + 1867776 z^5 + 65536 z^6) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] + 7315 Sqrt[2] (-1463 + 210672 z + 3511200 z^2 + 10700800 z^3 + 8755200 z^4 + 1867776 z^5 + 65536 z^6) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - 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