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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=-3/4





http://functions.wolfram.com/07.23.03.a8f6.01









  


  








Input Form





Hypergeometric2F1[-(21/4), -(3/4), 4, z] == (256 ((21216 + 21216 Sqrt[z] - 324207 z - 324207 z^(3/2) + 3212235 z^2 + 3212235 z^(5/2) + 65920030 z^3 + 65920030 z^(7/2) + 36859350 z^4 + 36859350 z^(9/2) - 6199347 z^5 - 6199347 z^(11/2) + 1381919 z^6 + 1381919 z^(13/2) - 226380 z^7 - 226380 z^(15/2) + 18480 z^8 + 18480 z^(17/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - (21216 - 329511 z + 3291795 z^2 + 17428210 z^3 - 17854210 z^4 - 3152787 z^5 + 700007 z^6 - 113960 z^7 + 9240 z^8) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))/(6106975875 Pi Sqrt[1 + Sqrt[z]] z^3)








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