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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=-21/4





http://functions.wolfram.com/07.23.03.9006.01









  


  










Input Form





Hypergeometric2F1[-(23/4), -(21/4), 5, z] == (1/(834833040166125 Pi z^4)) (4096 Sqrt[1 + Sqrt[z]] (16 (-59432 + 1775531 z - 31914984 z^2 + 598034500 z^3 + 43510755000 z^4 + 206090589714 z^5 + 283531288488 z^6 + 133092197988 z^7 + 19770519600 z^8 + 631580955 z^9) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (950912 - 950912 Sqrt[z] - 27695312 z + 27695312 z^(3/2) + 489979695 z^2 - 489979695 z^(5/2) - 9204270985 z^3 + 9204270985 z^(7/2) - 295385739045 z^4 + 295385739045 z^(9/2) - 1033483188429 z^5 + 1033483188429 z^(11/2) - 1044976203411 z^6 + 1044976203411 z^(13/2) - 336778268955 z^7 + 336778268955 z^(15/2) - 29112289335 z^8 + 29112289335 z^(17/2) - 302344575 z^9 + 302344575 z^(19/2)) EllipticK[(2 Sqrt[z])/(1 + Sqrt[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