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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=5





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









  


  










Input Form





Hypergeometric2F1[5, 5, -(23/4), z] == (1/161296154624) (-((1/(-1 + z)^15) (8 (20162019328 - 390091243520 z + 3764115210240 z^2 - 24807819182080 z^3 + 132407864852480 z^4 - 687470656094208 z^5 + 5260472483840000 z^6 + 30462912337386875 z^7 + 26874834068064060 z^8 + 5785967550640480 z^9 + 225295616072320 z^10))) - (1/(1 - z)^(63/4)) (157437950670 Sqrt[2] z^(27/4) (606515 + 1252160 z + 643968 z^2 + 88064 z^3 + 2048 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)^(63/4)) (157437950670 Sqrt[2] z^(27/4) (606515 + 1252160 z + 643968 z^2 + 88064 z^3 + 2048 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)^(63/4)) (78718975335 Sqrt[2] z^(27/4) (606515 + 1252160 z + 643968 z^2 + 88064 z^3 + 2048 z^4) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]]) + (1/(1 - z)^(63/4)) (78718975335 Sqrt[2] z^(27/4) (606515 + 1252160 z + 643968 z^2 + 88064 z^3 + 2048 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