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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.a84w.01









  


  










Input Form





Hypergeometric2F1[-(21/4), -(21/4), -(9/2), z] == (1/(40320 Pi^(3/2))) ((4 (5040 - 30240 z + 76125 z^2 - 104013 z^3 + 84627 z^4 - 52019 z^5) EllipticE[(1/2) (1 - Sqrt[z])] + 4 (5040 - 30240 z + 76125 z^2 - 104013 z^3 + 84627 z^4 - 52019 z^5) EllipticE[(1/2) (1 + Sqrt[z])] + (-10080 - 5040 Sqrt[z] + 60480 z + 29820 z^(3/2) - 152250 z^2 - 73815 z^(5/2) + 208026 z^3 + 98793 z^(7/2) - 169254 z^4 - 78413 z^(9/2) + 104038 z^5 + 69615 z^(11/2)) EllipticK[(1/2) (1 - Sqrt[z])] + (-10080 + 5040 Sqrt[z] + 60480 z - 29820 z^(3/2) - 152250 z^2 + 73815 z^(5/2) + 208026 z^3 - 98793 z^(7/2) - 169254 z^4 + 78413 z^(9/2) + 104038 z^5 - 69615 z^(11/2)) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[1/4]^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