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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=-21/4, b>=a > For fixed z and a=-21/4, b=17/4





http://functions.wolfram.com/07.23.03.a8u7.01









  


  








Input Form





Hypergeometric2F1[-(21/4), 17/4, 5, z] == (4096 (-2 (22848 + 22848 Sqrt[z] + 21896 z + 21896 z^(3/2) + 51051 z^2 + 51051 z^(5/2) + 258825 z^3 + 258825 z^(7/2) - 11790515 z^4 - 11790515 z^(9/2) + 44983719 z^5 + 44983719 z^(11/2) - 74370912 z^6 - 74370912 z^(13/2) + 63865648 z^7 + 63865648 z^(15/2) - 28089600 z^8 - 28089600 z^(17/2) + 5026560 z^9 + 5026560 z^(19/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (45696 + 32368 z + 87941 z^2 + 487305 z^3 - 13690345 z^4 + 49180483 z^5 - 78658536 z^6 + 65997008 z^7 - 28508480 z^8 + 5026560 z^9) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))/(20541646125 Pi Sqrt[1 + Sqrt[z]] z^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