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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=13/4





http://functions.wolfram.com/07.23.03.aa47.01









  


  








Input Form





Hypergeometric2F1[-(9/2), 13/4, 4, z] == (1/(225225 Pi Sqrt[1 + Sqrt[1 - z]] z^3)) (Sqrt[2] (2 (1 - z)^(1/4) (-7168 - 9408 z - 31584 z^2 + 773440 z^3 - 2167200 z^4 + 2555652 z^5 - 1413258 z^6 + 302841 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (-7168 - 9408 z - 31584 z^2 + 773440 z^3 - 2167200 z^4 + 2555652 z^5 - 1413258 z^6 + 302841 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (7168 + 9408 z + 31584 z^2 - 773440 z^3 + 2167200 z^4 - 2555652 z^5 + 1413258 z^6 - 302841 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (7168 + 9408 z + 31584 z^2 - 773440 z^3 + 2167200 z^4 - 2555652 z^5 + 1413258 z^6 - 302841 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (7168 + 9408 z + 31584 z^2 - 773440 z^3 + 2167200 z^4 - 2555652 z^5 + 1413258 z^6 - 302841 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (7168 + 5824 z + 26208 z^2 - 340000 z^3 + 847040 z^4 - 932292 z^5 + 490314 z^6 - 100947 z^7) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))








Standard Form





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MathML Form







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</math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02