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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=-15/4





http://functions.wolfram.com/07.23.03.a7ww.01









  


  










Input Form





Hypergeometric2F1[-(11/2), -(15/4), 1, z] == (1/(11088 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]])) (2 (1 - z)^(1/4) (69760 + 899472 z + 1825056 z^2 + 735680 z^3 + 27720 z^4 - 693 z^5) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (69760 + 899472 z + 1825056 z^2 + 735680 z^3 + 27720 z^4 - 693 z^5) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-25408 + 44624 z + 1345008 z^2 + 1796320 z^3 + 396220 z^4 + 231 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (-69760 - 899472 z - 1825056 z^2 - 735680 z^3 - 27720 z^4 + 693 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (-69760 - 899472 z - 1825056 z^2 - 735680 z^3 - 27720 z^4 + 693 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (-69760 - 899472 z - 1825056 z^2 - 735680 z^3 - 27720 z^4 + 693 z^5) 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