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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=-23/4, b>=a > For fixed z and a=-23/4, b=-11/4





http://functions.wolfram.com/07.23.03.9214.01









  


  










Input Form





Hypergeometric2F1[-(23/4), -(11/4), 21/4, z] == (221 (8 (1 - z)^(3/4) z^(1/4) (-216531315 + 4490526348 z - 52387993504 z^2 + 555362477824 z^3 + 17158927091712 z^4 + 32559356579840 z^5 + 12304933126144 z^6 + 383435931648 z^7 - 18085838848 z^8 + 645922816 z^9) - 3028410 Sqrt[2] (143 - 3080 z + 36960 z^2 - 394240 z^3 + 11038720 z^4 + 52985856 z^5 + 50462720 z^6 + 10485760 z^7) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 3028410 Sqrt[2] (143 - 3080 z + 36960 z^2 - 394240 z^3 + 11038720 z^4 + 52985856 z^5 + 50462720 z^6 + 10485760 z^7) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 1514205 Sqrt[2] (143 - 3080 z + 36960 z^2 - 394240 z^3 + 11038720 z^4 + 52985856 z^5 + 50462720 z^6 + 10485760 z^7) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] + 1514205 Sqrt[2] (143 - 3080 z + 36960 z^2 - 394240 z^3 + 11038720 z^4 + 52985856 z^5 + 50462720 z^6 + 10485760 z^7) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]]))/ (59109745109237760 z^(17/4))










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