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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=3/4





http://functions.wolfram.com/07.23.03.aa1w.01









  


  










Input Form





Hypergeometric2F1[-(9/2), 3/4, 5, z] == (8 Sqrt[2] (2 (-86016 + 781312 z - 3247552 z^2 + 8675520 z^3 + 5601440 z^4 - 3493568 z^5 + 1493076 z^6 - 379236 z^7 + 43095 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (-86016 + 781312 z - 3247552 z^2 + 8675520 z^3 + 5601440 z^4 - 3493568 z^5 + 1493076 z^6 - 379236 z^7 + 43095 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (-86016 + 781312 z - 3247552 z^2 + 8675520 z^3 + 5601440 z^4 - 3493568 z^5 + 1493076 z^6 - 379236 z^7 + 43095 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (-86016 + 781312 z - 3247552 z^2 + 8675520 z^3 + 5601440 z^4 - 3493568 z^5 + 1493076 z^6 - 379236 z^7 + 43095 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (-86016 + 781312 z - 3247552 z^2 + 8675520 z^3 + 5601440 z^4 - 3493568 z^5 + 1493076 z^6 - 379236 z^7 + 43095 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (86016 - 738304 z + 2891840 z^2 - 7338240 z^3 + 3571360 z^4 - 2517632 z^5 + 1217268 z^6 - 344760 z^7 + 43095 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (49774725 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