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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=-7/4





http://functions.wolfram.com/07.23.03.a8d3.01









  


  










Input Form





Hypergeometric2F1[-(21/4), -(7/4), 6, -z] == (1/(2429094845902725 Pi z^5)) (16384 (1 + z)^(1/4) (2 (-3168256 - 54206880 z - 475837089 z^2 - 3087109662 z^3 - 21016336887 z^4 + 418828828308 z^5 - 450182173815 z^6 + 60665714802 z^7 + 3385055751 z^8 + 259231896 z^9 + 12113640 z^10) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - Sqrt[1 + z] (-3168256 - 51830688 z - 437335353 z^2 - 2765042826 z^3 - 18991598535 z^4 + 136246228008 z^5 - 81900738711 z^6 + 1579012974 z^7 + 124063863 z^8 + 6056820 z^9) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] - (-3168256 - 54206880 z - 475837089 z^2 - 3087109662 z^3 - 21016336887 z^4 + 418828828308 z^5 - 450182173815 z^6 + 60665714802 z^7 + 3385055751 z^8 + 259231896 z^9 + 12113640 z^10) EllipticK[1/2 - 1/(2 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