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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=-11/2, b>=a > For fixed z and a=-11/2, b=-19/4





http://functions.wolfram.com/07.23.03.a7wf.01









  


  










Input Form





Hypergeometric2F1[-(11/2), -(19/4), 3, z] == (2 (1 - z)^(1/4) (-374528 + 18820032 z + 1779350976 z^2 + 10601422880 z^3 + 15811843920 z^4 + 6807878748 z^5 + 705318768 z^6 + 5753979 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (-374528 + 18820032 z + 1779350976 z^2 + 10601422880 z^3 + 15811843920 z^4 + 6807878748 z^5 + 705318768 z^6 + 5753979 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (-374528 + 18820032 z + 1779350976 z^2 + 10601422880 z^3 + 15811843920 z^4 + 6807878748 z^5 + 705318768 z^6 + 5753979 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (-374528 + 18820032 z + 1779350976 z^2 + 10601422880 z^3 + 15811843920 z^4 + 6807878748 z^5 + 705318768 z^6 + 5753979 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (-374528 + 18820032 z + 1779350976 z^2 + 10601422880 z^3 + 15811843920 z^4 + 6807878748 z^5 + 705318768 z^6 + 5753979 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (374528 - 19007296 z - 352680192 z^2 + 2455122400 z^3 + 14087374960 z^4 + 15062807052 z^5 + 4251935556 z^6 + 244087767 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (354323970 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z^2)










Standard Form





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MathML Form







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





2007-05-02