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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=-15/4





http://functions.wolfram.com/07.23.03.9128.01









  


  








Input Form





Hypergeometric2F1[-(23/4), -(15/4), 21/4, z] == (221 (-8 (1 - z)^(3/4) z^(1/4) (216531315 - 5156776548 z + 70509998944 z^2 - 899088358784 z^3 - 38608616761344 z^4 - 106369788452864 z^5 - 72637195550720 z^6 - 12027197915136 z^7 - 146624479232 z^8 + 2583691264 z^9) - 3028410 Sqrt[2] (143 - 3520 z + 49280 z^2 - 630784 z^3 + 22077440 z^4 + 141295616 z^5 + 201850880 z^6 + 83886080 z^7 + 8388608 z^8) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 3028410 Sqrt[2] (143 - 3520 z + 49280 z^2 - 630784 z^3 + 22077440 z^4 + 141295616 z^5 + 201850880 z^6 + 83886080 z^7 + 8388608 z^8) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 1514205 Sqrt[2] (143 - 3520 z + 49280 z^2 - 630784 z^3 + 22077440 z^4 + 141295616 z^5 + 201850880 z^6 + 83886080 z^7 + 8388608 z^8) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] + 1514205 Sqrt[2] (143 - 3520 z + 49280 z^2 - 630784 z^3 + 22077440 z^4 + 141295616 z^5 + 201850880 z^6 + 83886080 z^7 + 8388608 z^8) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]]))/ (126100789566373888 z^(17/4))








Standard Form





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MathML Form







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Date Added to functions.wolfram.com (modification date)





2007-05-02