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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.aa2s.01









  


  








Input Form





Hypergeometric2F1[-(9/2), 7/4, 5, z] == (8 Sqrt[2] (2 (28672 - 179200 z + 407232 z^2 - 188160 z^3 + 666080 z^4 - 781184 z^5 + 490620 z^6 - 164424 z^7 + 23205 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (28672 - 179200 z + 407232 z^2 - 188160 z^3 + 666080 z^4 - 781184 z^5 + 490620 z^6 - 164424 z^7 + 23205 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (28672 - 179200 z + 407232 z^2 - 188160 z^3 + 666080 z^4 - 781184 z^5 + 490620 z^6 - 164424 z^7 + 23205 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (28672 - 179200 z + 407232 z^2 - 188160 z^3 + 666080 z^4 - 781184 z^5 + 490620 z^6 - 164424 z^7 + 23205 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (28672 - 179200 z + 407232 z^2 - 188160 z^3 + 666080 z^4 - 781184 z^5 + 490620 z^6 - 164424 z^7 + 23205 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (-28672 + 164864 z - 329280 z^2 + 47040 z^3 + 274720 z^4 - 480896 z^5 + 373932 z^6 - 145860 z^7 + 23205 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (3828825 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