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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=21/4





http://functions.wolfram.com/07.23.03.a8xe.01









  


  








Input Form





Hypergeometric2F1[-(21/4), 21/4, 4, -z] == (1/(111035925 Pi z^3)) (256 (1 + z)^(1/4) (2 (224 - 2121 z + 24906 z^2 + 2149103 z^3 + 12708300 z^4 + 30022608 z^5 + 34870528 z^6 + 19928832 z^7 + 4494336 z^8) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - Sqrt[1 + z] (224 - 2289 z + 26649 z^2 + 1261370 z^3 + 5842320 z^4 + 10267488 z^5 + 7904512 z^6 + 2247168 z^7) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] - (224 - 2121 z + 24906 z^2 + 2149103 z^3 + 12708300 z^4 + 30022608 z^5 + 34870528 z^6 + 19928832 z^7 + 4494336 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