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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.aa69.01









  


  








Input Form





Hypergeometric2F1[-(9/2), 21/4, 4, z] == (Sqrt[2] (2 (1 - z)^(1/4) (-7168 - 63168 z - 663264 z^2 + 37218112 z^3 - 172254912 z^4 + 301629636 z^5 - 231572418 z^6 + 65716497 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (-7168 - 63168 z - 663264 z^2 + 37218112 z^3 - 172254912 z^4 + 301629636 z^5 - 231572418 z^6 + 65716497 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (7168 + 63168 z + 663264 z^2 - 37218112 z^3 + 172254912 z^4 - 301629636 z^5 + 231572418 z^6 - 65716497 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (7168 + 63168 z + 663264 z^2 - 37218112 z^3 + 172254912 z^4 - 301629636 z^5 + 231572418 z^6 - 65716497 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (7168 + 63168 z + 663264 z^2 - 37218112 z^3 + 172254912 z^4 - 301629636 z^5 + 231572418 z^6 - 65716497 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (7168 + 59584 z + 631008 z^2 - 17646112 z^3 + 70717088 z^4 - 113223204 z^5 + 81363282 z^6 - 21905499 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (9954945 Pi Sqrt[1 + Sqrt[1 - z]] z^3)








Standard Form





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MathML Form







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





2007-05-02