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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=-13/4, b>=a > For fixed z and a=-13/4, b=11/2





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









  


  








Input Form





Hypergeometric2F1[-(13/4), 11/2, 5, z] == (128 Sqrt[2] (-2 (3328 + 12480 z + 48828 z^2 + 295360 z^3 - 9680975 z^4 + 27702741 z^5 - 27760425 z^6 + 9388071 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (3328 + 12480 z + 48828 z^2 + 295360 z^3 - 9680975 z^4 + 27702741 z^5 - 27760425 z^6 + 9388071 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (-3328 - 14144 z - 56420 z^2 - 326040 z^3 + 3987625 z^4 - 6720186 z^5 + 3129357 z^6) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (3328 + 12480 z + 48828 z^2 + 295360 z^3 - 9680975 z^4 + 27702741 z^5 - 27760425 z^6 + 9388071 z^7) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (3328 + 12480 z + 48828 z^2 + 295360 z^3 - 9680975 z^4 + 27702741 z^5 - 27760425 z^6 + 9388071 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (3328 + 12480 z + 48828 z^2 + 295360 z^3 - 9680975 z^4 + 27702741 z^5 - 27760425 z^6 + 9388071 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (353296125 Pi Sqrt[1 + Sqrt[1 - z]] z^4)








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