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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=-3/4





http://functions.wolfram.com/07.23.03.a8f3.01









  


  








Input Form





Hypergeometric2F1[-(21/4), -(3/4), 3, -z] == (1/(111035925 Pi z^2)) (64 (1 + z)^(1/4) (-2 (7956 + 157131 z - 5069992 z^2 + 3782130 z^3 + 785400 z^4 + 208747 z^5 + 39732 z^6 + 3696 z^7) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] + 4 Sqrt[1 + z] (1989 + 37791 z - 428140 z^2 + 78210 z^3 + 21945 z^4 + 4543 z^5 + 462 z^6) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] + (7956 + 157131 z - 5069992 z^2 + 3782130 z^3 + 785400 z^4 + 208747 z^5 + 39732 z^6 + 3696 z^7) EllipticK[1/2 - 1/(2 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