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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=-47/8, b>=a > For fixed z and a=-47/8, b=-11/8





http://functions.wolfram.com/07.23.03.b4x5.01









  


  










Input Form





Hypergeometric2F1[-(47/8), -(11/8), 5, z] == (65536 2^(1/4) (-8 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (334573824 - 5809735048 z + 55589353729 z^2 - 491411838645 z^3 - 8401478825600 z^4 - 7850974679674 z^5 - 122989800087 z^6 + 18389316231 z^7 - 2183032170 z^8 + 135883440 z^9) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 4 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (334573824 - 5809735048 z + 55589353729 z^2 - 491411838645 z^3 - 8401478825600 z^4 - 7850974679674 z^5 - 122989800087 z^6 + 18389316231 z^7 - 2183032170 z^8 + 135883440 z^9) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 4 Sqrt[1 - z] (334573824 - 5809735048 z + 55589353729 z^2 - 491411838645 z^3 - 8401478825600 z^4 - 7850974679674 z^5 - 122989800087 z^6 + 18389316231 z^7 - 2183032170 z^8 + 135883440 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (1338295296 - 23740800928 z + 230934789943 z^2 - 2046721388166 z^3 + 33606626735605 z^4 + 83627703658604 z^5 + 20835332276913 z^6 - 2105221591638 z^7 + 310734449091 z^8 - 35970287760 z^9 + 2174135040 z^10) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/(2178973905647564025 Pi (1 + Sqrt[1 - z])^(1/4) 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