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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=-23/4, b>=a > For fixed z and a=-23/4, b=3/2





http://functions.wolfram.com/07.23.03.9622.01









  


  










Input Form





Hypergeometric2F1[-(23/4), 3/2, 2, z] == (1/(4542615 Pi Sqrt[1 + Sqrt[1 - z]] z)) (4 Sqrt[2] (-2 (1 - z)^(1/4) (168245 - 2162508 z + 6622119 z^2 - 9840362 z^3 + 7927491 z^4 - 3341520 z^5 + 580125 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (168245 - 2162508 z + 6622119 z^2 - 9840362 z^3 + 7927491 z^4 - 3341520 z^5 + 580125 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (168245 - 2162508 z + 6622119 z^2 - 9840362 z^3 + 7927491 z^4 - 3341520 z^5 + 580125 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (168245 - 2162508 z + 6622119 z^2 - 9840362 z^3 + 7927491 z^4 - 3341520 z^5 + 580125 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (168245 - 2162508 z + 6622119 z^2 - 9840362 z^3 + 7927491 z^4 - 3341520 z^5 + 580125 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (168245 + 24677 z - 2391327 z^2 + 7556173 z^3 - 10936913 z^4 + 8502975 z^5 - 3457545 z^6 + 580125 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))










Standard Form





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MathML Form







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Date Added to functions.wolfram.com (modification date)





2007-05-02