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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=-41/8, b>=a > For fixed z and a=-41/8, b=-19/8





http://functions.wolfram.com/07.23.03.b8sp.01









  


  










Input Form





Hypergeometric2F1[-(41/8), -(19/8), 5, z] == (1/(6881476473246375 Pi z^4)) (32768 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (-2309120 + 44667040 z - 486798125 z^2 + 5057383210 z^3 + 311266463205 z^4 + 645121923192 z^5 + 258963980301 z^6 + 9457109970 z^7 - 423314661 z^8 + 15853068 z^9) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-288640 + 5536025 z - 59955940 z^2 + 42623804795 z^3 + 118284859530 z^4 + 74546124399 z^5 + 10470664440 z^6 - 70395171 z^7 + 2642178 z^8) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (288640 - 5373665 z + 56965810 z^2 + 69410846065 z^3 + 162796790880 z^4 + 71999690481 z^5 + 3129471114 z^6 - 140224161 z^7 + 5284356 z^8) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 2 (-2309120 + 44667040 z - 486798125 z^2 + 5057383210 z^3 + 311266463205 z^4 + 645121923192 z^5 + 258963980301 z^6 + 9457109970 z^7 - 423314661 z^8 + 15853068 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))










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