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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=-7/4, b>=a > For fixed z and a=-7/4, b=5/2





http://functions.wolfram.com/07.23.03.af4u.01









  


  










Input Form





Hypergeometric2F1[-(7/4), 5/2, 5, z] == (1/(504735 Pi Sqrt[1 + Sqrt[1 - z]] z^4)) (1024 Sqrt[2] (-2 (1 - z)^(1/4) (224 - 560 z + 196 z^2 + 266 z^3 - 516 z^4 + 195 z^5) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] - 2 (1 - z)^(3/4) (224 - 560 z + 196 z^2 + 266 z^3 - 516 z^4 + 195 z^5) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (224 - 560 z + 196 z^2 + 266 z^3 - 516 z^4 + 195 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (224 - 560 z + 196 z^2 + 266 z^3 - 516 z^4 + 195 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (224 - 560 z + 196 z^2 + 266 z^3 - 516 z^4 + 195 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (224 - 672 z + 455 z^2 + 210 z^3 + 338 z^4 - 555 z^5 + 195 z^6) 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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Rule Form





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





2007-05-02