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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.a92y.01









  


  










Input Form





Hypergeometric2F1[-(19/4), -(15/4), 5, z] == (1/(903648774105 Pi z^4)) (4096 (2 Sqrt[1 - z] (-4224 + 93104 z - 1196811 z^2 + 15492246 z^3 + 361275143 z^4 + 760931028 z^5 + 382930611 z^6 + 41764742 z^7 + 211761 z^8) EllipticE[(1/2) (1 - Sqrt[1 - z])] - Sqrt[1 - z] (-4224 + 93104 z - 1196811 z^2 + 15492246 z^3 + 361275143 z^4 + 760931028 z^5 + 382930611 z^6 + 41764742 z^7 + 211761 z^8) EllipticK[(1/2) (1 - Sqrt[1 - z])] + 2 (2112 - 48136 z + 633171 z^2 - 8191722 z^3 + 45748781 z^4 + 527699724 z^5 + 728602557 z^6 + 249474950 z^7 + 17576163 z^8) EllipticK[(1/2) (1 - 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