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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=-39/8, b>=a > For fixed z and a=-39/8, b=-11/8





http://functions.wolfram.com/07.23.03.b9x4.01









  


  










Input Form





Hypergeometric2F1[-(39/8), -(11/8), 6, z] == (524288 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (303726592 - 4680474240 z + 36500311679 z^2 - 206721260746 z^3 + 1201604287065 z^4 + 13084560747748 z^5 + 8225099237985 z^6 + 69721307766 z^7 - 6186174489 z^8 + 330002640 z^9) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (303726592 - 4680474240 z + 36500311679 z^2 - 206721260746 z^3 + 1201604287065 z^4 + 13084560747748 z^5 + 8225099237985 z^6 + 69721307766 z^7 - 6186174489 z^8 + 330002640 z^9) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (303726592 - 4680474240 z + 36500311679 z^2 - 206721260746 z^3 + 1201604287065 z^4 + 13084560747748 z^5 + 8225099237985 z^6 + 69721307766 z^7 - 6186174489 z^8 + 330002640 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (303726592 - 4794371712 z + 38224345679 z^2 - 219945491350 z^3 + 1275626187381 z^4 - 15607900890092 z^5 - 26159929574583 z^6 - 4389191863254 z^7 + 290601699795 z^8 - 25377203016 z^9 + 1320010560 z^10) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/(7408511279201717685 Pi (1 + Sqrt[1 - z])^(1/4) z^5)










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