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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=-9/2, b>=a > For fixed z and a=-9/2, b=21/4





http://functions.wolfram.com/07.23.03.aa67.01









  


  








Input Form





Hypergeometric2F1[-(9/2), 21/4, 3, z] == (2 (1 - z)^(1/4) (-13440 - 288960 z + 25978928 z^2 - 161724960 z^3 + 356141016 z^4 - 329625604 z^5 + 109527495 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (-13440 - 288960 z + 25978928 z^2 - 161724960 z^3 + 356141016 z^4 - 329625604 z^5 + 109527495 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (13440 + 288960 z - 25978928 z^2 + 161724960 z^3 - 356141016 z^4 + 329625604 z^5 - 109527495 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (13440 + 288960 z - 25978928 z^2 + 161724960 z^3 - 356141016 z^4 + 329625604 z^5 - 109527495 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (13440 + 288960 z - 25978928 z^2 + 161724960 z^3 - 356141016 z^4 + 329625604 z^5 - 109527495 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (13440 + 282240 z - 12851408 z^2 + 68500624 z^3 - 136270584 z^4 + 116829328 z^5 - 36509165 z^6) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (3318315 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z^2)








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