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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=-17/4, b>=a > For fixed z and a=-17/4, b=9/2





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









  


  








Input Form





Hypergeometric2F1[-(17/4), 9/2, 4, z] == (16 Sqrt[2] (2 (-42432 - 236028 z - 1833858 z^2 + 80426815 z^3 - 314567800 z^4 + 480594246 z^5 - 328885326 z^6 + 84492639 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (-42432 - 236028 z - 1833858 z^2 + 80426815 z^3 - 314567800 z^4 + 480594246 z^5 - 328885326 z^6 + 84492639 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (42432 + 257244 z + 1969110 z^2 - 35236735 z^3 + 91649825 z^4 - 86828841 z^5 + 28164213 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (-42432 - 236028 z - 1833858 z^2 + 80426815 z^3 - 314567800 z^4 + 480594246 z^5 - 328885326 z^6 + 84492639 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (-42432 - 236028 z - 1833858 z^2 + 80426815 z^3 - 314567800 z^4 + 480594246 z^5 - 328885326 z^6 + 84492639 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (-42432 - 236028 z - 1833858 z^2 + 80426815 z^3 - 314567800 z^4 + 480594246 z^5 - 328885326 z^6 + 84492639 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (353296125 Pi Sqrt[1 + Sqrt[1 - z]] z^3)








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