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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=-19/4, b>=a > For fixed z and a=-19/4, b=-15/4





http://functions.wolfram.com/07.23.03.a92w.01









  


  








Input Form





Hypergeometric2F1[-(19/4), -(15/4), 17/4, z] == (1/(123145302310912 z^(13/4))) (117 (8 (1 - z)^(3/4) z^(1/4) (3620925 - 87224060 z + 1444507680 z^2 + 72153830784 z^3 + 198917920768 z^4 + 122647437312 z^5 + 15906963456 z^6 + 100925440 z^7) - 14630 Sqrt[2] (-495 + 12320 z - 206976 z^2 + 8279040 z^3 + 55193600 z^4 + 75694080 z^5 + 27525120 z^6 + 2097152 z^7) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 14630 Sqrt[2] (-495 + 12320 z - 206976 z^2 + 8279040 z^3 + 55193600 z^4 + 75694080 z^5 + 27525120 z^6 + 2097152 z^7) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 7315 Sqrt[2] (-495 + 12320 z - 206976 z^2 + 8279040 z^3 + 55193600 z^4 + 75694080 z^5 + 27525120 z^6 + 2097152 z^7) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] + 7315 Sqrt[2] (-495 + 12320 z - 206976 z^2 + 8279040 z^3 + 55193600 z^4 + 75694080 z^5 + 27525120 z^6 + 2097152 z^7) 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