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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=-1/4





http://functions.wolfram.com/07.23.03.a9c3.01









  


  








Input Form





Hypergeometric2F1[-(19/4), -(1/4), 5, -z] == (1/(466821830475 Pi z^4)) (4096 (1 + z)^(1/4) (-8 (20064 + 244948 z + 1521520 z^2 + 7658805 z^3 - 67762230 z^4 + 1733082 z^5 + 429624 z^6 + 76245 z^7 + 6630 z^8) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] + 4 (20064 + 244948 z + 1521520 z^2 + 7658805 z^3 - 67762230 z^4 + 1733082 z^5 + 429624 z^6 + 76245 z^7 + 6630 z^8) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] - Sqrt[1 + z] (-80256 - 919600 z - 5405785 z^2 - 26685120 z^3 + 62527530 z^4 + 11644932 z^5 + 3013335 z^6 + 570180 z^7 + 53040 z^8) 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