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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=5/4





http://functions.wolfram.com/07.23.03.a80f.01









  


  










Input Form





Hypergeometric2F1[-(11/2), 5/4, 3, z] == (2 (1 - z)^(1/4) (59136 - 310464 z + 1580736 z^2 - 3003872 z^3 + 3210864 z^4 - 2009964 z^5 + 690536 z^6 - 100947 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (59136 - 310464 z + 1580736 z^2 - 3003872 z^3 + 3210864 z^4 - 2009964 z^5 + 690536 z^6 - 100947 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-59136 + 340032 z - 649344 z^2 + 1155296 z^3 - 1178608 z^4 + 710724 z^5 - 236588 z^6 + 33649 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (-59136 + 310464 z - 1580736 z^2 + 3003872 z^3 - 3210864 z^4 + 2009964 z^5 - 690536 z^6 + 100947 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (-59136 + 310464 z - 1580736 z^2 + 3003872 z^3 - 3210864 z^4 + 2009964 z^5 - 690536 z^6 + 100947 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (-59136 + 310464 z - 1580736 z^2 + 3003872 z^3 - 3210864 z^4 + 2009964 z^5 - 690536 z^6 + 100947 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (270270 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