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





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









  


  










Input Form





Hypergeometric2F1[6, 6, -(13/4), z] == (1/104689827840) (-((1/(-1 + z)^15) (8 (13086228480 - 341248573440 z + 5126781665280 z^2 - 71788566413312 z^3 + 2835600692477952 z^4 + 19975444017411015 z^5 + 32702366514396880 z^6 + 16748354761819440 z^7 + 2533958460172032 z^8 + 73945123061248 z^9))) - (1/(1 - z)^(61/4)) (8216658450 Sqrt[2] z^(17/4) (1239315 + 5901500 z + 7553920 z^2 + 3125760 z^3 + 378880 z^4 + 8192 z^5) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))]) - (1/(1 - z)^(61/4)) (8216658450 Sqrt[2] z^(17/4) (1239315 + 5901500 z + 7553920 z^2 + 3125760 z^3 + 378880 z^4 + 8192 z^5) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))]) + (1/(1 - z)^(61/4)) (4108329225 Sqrt[2] z^(17/4) (1239315 + 5901500 z + 7553920 z^2 + 3125760 z^3 + 378880 z^4 + 8192 z^5) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]]) - (1/(1 - z)^(61/4)) (4108329225 Sqrt[2] z^(17/4) (1239315 + 5901500 z + 7553920 z^2 + 3125760 z^3 + 378880 z^4 + 8192 z^5) 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