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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=-11/4





http://functions.wolfram.com/07.23.03.a7xj.01









  


  








Input Form





Hypergeometric2F1[-(11/2), -(11/4), 3, z] == (2 (1 - z)^(1/4) (-59136 + 2084544 z + 116953152 z^2 + 373759840 z^3 + 223242000 z^4 + 13886796 z^5 - 713944 z^6 + 30723 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (-59136 + 2084544 z + 116953152 z^2 + 373759840 z^3 + 223242000 z^4 + 13886796 z^5 - 713944 z^6 + 30723 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (59136 - 2114112 z - 13213824 z^2 + 189863840 z^3 + 415262960 z^4 + 139096284 z^5 + 239932 z^6 - 10241 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (-59136 + 2084544 z + 116953152 z^2 + 373759840 z^3 + 223242000 z^4 + 13886796 z^5 - 713944 z^6 + 30723 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (-59136 + 2084544 z + 116953152 z^2 + 373759840 z^3 + 223242000 z^4 + 13886796 z^5 - 713944 z^6 + 30723 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (-59136 + 2084544 z + 116953152 z^2 + 373759840 z^3 + 223242000 z^4 + 13886796 z^5 - 713944 z^6 + 30723 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (25675650 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