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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 8 and fixed z and a<0 > For fixed z and a=-45/8, b>=a > For fixed z and a=-45/8, b=-15/8





http://functions.wolfram.com/07.23.03.b6eh.01









  


  










Input Form





Hypergeometric2F1[-(45/8), -(15/8), 4, z] == (2048 2^(1/4) (-2 Sqrt[1 - z] (-14421120 + 295294965 z - 4319238105 z^2 - 90740880502 z^3 - 124635882890 z^4 - 16706798535 z^5 + 1558414795 z^6 - 157915240 z^7 + 9223368 z^8) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-14421120 + 295294965 z - 4319238105 z^2 - 90740880502 z^3 - 124635882890 z^4 - 16706798535 z^5 + 1558414795 z^6 - 157915240 z^7 + 9223368 z^8) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (-14421120 + 304308165 z - 4502318730 z^2 + 139426616603 z^3 + 521689418720 z^4 + 281703081035 z^5 + 267367870 z^6 - 26776715 z^7 + 1537228 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[1 - z] (-14421120 + 295294965 z - 4319238105 z^2 - 90740880502 z^3 - 124635882890 z^4 - 16706798535 z^5 + 1558414795 z^6 - 157915240 z^7 + 9223368 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (232957500830145 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^3)










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