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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=-9/2, b>=a > For fixed z and a=-9/2, b=5/4





http://functions.wolfram.com/07.23.03.aa2a.01









  


  








Input Form





Hypergeometric2F1[-(9/2), 5/4, 3, z] == (2 (1 - z)^(1/4) (13440 - 60480 z + 252368 z^2 - 382752 z^3 + 306504 z^4 - 127820 z^5 + 21945 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (13440 - 60480 z + 252368 z^2 - 382752 z^3 + 306504 z^4 - 127820 z^5 + 21945 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (-13440 + 60480 z - 252368 z^2 + 382752 z^3 - 306504 z^4 + 127820 z^5 - 21945 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (-13440 + 60480 z - 252368 z^2 + 382752 z^3 - 306504 z^4 + 127820 z^5 - 21945 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (-13440 + 60480 z - 252368 z^2 + 382752 z^3 - 306504 z^4 + 127820 z^5 - 21945 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-13440 + 67200 z - 101168 z^2 + 143536 z^3 - 109608 z^4 + 44000 z^5 - 7315 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)])/(45045 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z^2)








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