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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=-21/4, b>=a > For fixed z and a=-21/4, b=19/4





http://functions.wolfram.com/07.23.03.a8va.01









  


  








Input Form





Hypergeometric2F1[-(21/4), 19/4, 1, -z] == (1/(765765 Pi Sqrt[1 + Sqrt[1 + z]])) (2 Sqrt[2] (2 (814867 + 15579506 z + 79719424 z^2 + 165605376 z^3 + 150994944 z^4 + 50331648 z^5) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + 2 Sqrt[1 + z] (814867 + 15579506 z + 79719424 z^2 + 165605376 z^3 + 150994944 z^4 + 50331648 z^5) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (863969 + 11990336 z + 43382784 z^2 + 57409536 z^3 + 25165824 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 2 (814867 + 15579506 z + 79719424 z^2 + 165605376 z^3 + 150994944 z^4 + 50331648 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + 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