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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.anry.01









  


  










Input Form





Hypergeometric2F1[6, 6, -(9/4), z] == (1/8053063680) (-((1/(-1 + z)^14) (8 (-1006632960 + 30198988800 z - 632769478656 z^2 + 33189628215296 z^3 + 293522120990735 z^4 + 578122396302080 z^5 + 346149248581360 z^6 + 59973962818816 z^7 + 1973932885504 z^8))) + (1/(1 - z)^(57/4)) (222071850 Sqrt[2] z^(13/4) (569415 + 3349500 z + 5104000 z^2 + 2449920 z^3 + 337920 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)^(57/4)) (222071850 Sqrt[2] z^(13/4) (569415 + 3349500 z + 5104000 z^2 + 2449920 z^3 + 337920 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)^(57/4)) (111035925 Sqrt[2] z^(13/4) (569415 + 3349500 z + 5104000 z^2 + 2449920 z^3 + 337920 z^4 + 8192 z^5) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]]) + (1/(1 - z)^(57/4)) (111035925 Sqrt[2] z^(13/4) (569415 + 3349500 z + 5104000 z^2 + 2449920 z^3 + 337920 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