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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=-7/4





http://functions.wolfram.com/07.23.03.a9zv.01









  


  








Input Form





Hypergeometric2F1[-(9/2), -(7/4), 3, z] == (2 (1 - z)^(1/4) (-2688 + 64512 z + 1995664 z^2 + 2916624 z^3 + 338184 z^4 - 26488 z^5 + 1617 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] + 2 (1 - z)^(3/4) (-2688 + 64512 z + 1995664 z^2 + 2916624 z^3 + 338184 z^4 - 26488 z^5 + 1617 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (2688 - 65856 z + 18320 z^2 + 3042080 z^3 + 2281800 z^4 + 8932 z^5 - 539 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (-2688 + 64512 z + 1995664 z^2 + 2916624 z^3 + 338184 z^4 - 26488 z^5 + 1617 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] - Sqrt[1 - z] (-2688 + 64512 z + 1995664 z^2 + 2916624 z^3 + 338184 z^4 - 26488 z^5 + 1617 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (-2688 + 64512 z + 1995664 z^2 + 2916624 z^3 + 338184 z^4 - 26488 z^5 + 1617 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)])/(495495 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