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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=-11/2, b>=a > For fixed z and a=-11/2, b=-3/4





http://functions.wolfram.com/07.23.03.a7yv.01









  


  








Input Form





Hypergeometric2F1[-(11/2), -(3/4), 3, z] == (2 (1 - z)^(1/4) (-768 + 15552 z + 329152 z^2 + 171808 z^3 - 45552 z^4 + 12716 z^5 - 2464 z^6 + 231 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (-768 + 15552 z + 329152 z^2 + 171808 z^3 - 45552 z^4 + 12716 z^5 - 2464 z^6 + 231 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (768 - 15936 z + 38912 z^2 + 444640 z^3 + 15920 z^4 - 4388 z^5 + 836 z^6 - 77 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (-768 + 15552 z + 329152 z^2 + 171808 z^3 - 45552 z^4 + 12716 z^5 - 2464 z^6 + 231 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (-768 + 15552 z + 329152 z^2 + 171808 z^3 - 45552 z^4 + 12716 z^5 - 2464 z^6 + 231 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (-768 + 15552 z + 329152 z^2 + 171808 z^3 - 45552 z^4 + 12716 z^5 - 2464 z^6 + 231 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (90090 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z^2)








Standard Form





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MathML Form







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





2007-05-02