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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=5, b>=a > For fixed z and a=5, b=6





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









  


  








Input Form





Hypergeometric2F1[5, 6, -(21/4), z] == (1/207634825216) ((1/(-1 + z)^16) (8 (25954353152 - 563580239872 z + 6220320604160 z^2 - 48266037166080 z^3 + 319247939010560 z^4 - 2322411491950592 z^5 + 51903554893381632 z^6 + 208543824448555295 z^7 + 193152898002014740 z^8 + 52117522198041120 z^9 + 3316221055541120 z^10 + 7665959741440 z^11)) - (1/(1 - z)^(65/4)) (336882996450 Sqrt[2] z^(25/4) (483923 + 1334960 z + 970880 z^2 + 209920 z^3 + 10240 z^4) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))]) - (1/(1 - z)^(65/4)) (336882996450 Sqrt[2] z^(25/4) (483923 + 1334960 z + 970880 z^2 + 209920 z^3 + 10240 z^4) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))]) + (1/(1 - z)^(65/4)) (168441498225 Sqrt[2] z^(25/4) (483923 + 1334960 z + 970880 z^2 + 209920 z^3 + 10240 z^4) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]]) - (1/(1 - z)^(65/4)) (168441498225 Sqrt[2] z^(25/4) (483923 + 1334960 z + 970880 z^2 + 209920 z^3 + 10240 z^4) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/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