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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 4 and fixed z > For fixed z and a=1, b>=a > For fixed z and a=1, b=6





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









  


  










Input Form





Hypergeometric2F1[1, 6, -(7/4), z] == (1/2293760) ((1/(-1 + z)^8) (8 (286720 - 3276800 z + 25067520 z^2 + 35798455 z^3 - 15516116 z^4 + 5832288 z^5 - 1409408 z^6 + 157696 z^7)) - (281642130 Sqrt[2] z^(11/4) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(35/4) - (281642130 Sqrt[2] z^(11/4) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(35/4) - (140821065 Sqrt[2] z^(11/4) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/(1 - z)^(35/4) + (140821065 Sqrt[2] z^(11/4) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/(1 - z)^(35/4))










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