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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=-39/8





http://functions.wolfram.com/07.23.03.b66h.01









  


  










Input Form





Hypergeometric2F1[-(45/8), -(39/8), 4, z] == (2048 2^(1/4) (2 Sqrt[1 - z] (55349632 - 1849456063 z + 48264446685 z^2 + 2531961851773 z^3 + 11153227964345 z^4 + 13264128406035 z^5 + 4764623627335 z^6 + 425570332655 z^7 + 3119639523 z^8) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (55349632 - 1849456063 z + 48264446685 z^2 + 2531961851773 z^3 + 11153227964345 z^4 + 13264128406035 z^5 + 4764623627335 z^6 + 425570332655 z^7 + 3119639523 z^8) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (55349632 - 1849456063 z + 48264446685 z^2 + 2531961851773 z^3 + 11153227964345 z^4 + 13264128406035 z^5 + 4764623627335 z^6 + 425570332655 z^7 + 3119639523 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (-55349632 + 1884049583 z - 49414681225 z^2 + 2611765933787 z^3 + 25251552707795 z^4 + 55072749782765 z^5 + 37622324915045 z^6 + 7883202180425 z^7 + 362399109137 z^8) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (5236479475181955 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