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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=-11/4





http://functions.wolfram.com/07.23.03.a95g.01









  


  










Input Form





Hypergeometric2F1[-(19/4), -(11/4), 21/4, z] == (1/(1477743627730944 z^(17/4))) (221 (-8 (1 - z)^(3/4) z^(1/4) (9414405 - 174963096 z + 1807308272 z^2 - 16734660096 z^3 - 413051767296 z^4 - 625245011968 z^5 - 176563912704 z^6 - 3391094784 z^7 + 80740352 z^8) - 131670 Sqrt[2] (143 - 2772 z + 29568 z^2 - 275968 z^3 + 6623232 z^4 + 26492928 z^5 + 20185088 z^6 + 3145728 z^7) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 131670 Sqrt[2] (143 - 2772 z + 29568 z^2 - 275968 z^3 + 6623232 z^4 + 26492928 z^5 + 20185088 z^6 + 3145728 z^7) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 65835 Sqrt[2] (143 - 2772 z + 29568 z^2 - 275968 z^3 + 6623232 z^4 + 26492928 z^5 + 20185088 z^6 + 3145728 z^7) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] + 65835 Sqrt[2] (143 - 2772 z + 29568 z^2 - 275968 z^3 + 6623232 z^4 + 26492928 z^5 + 20185088 z^6 + 3145728 z^7) 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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Date Added to functions.wolfram.com (modification date)





2007-05-02