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





http://functions.wolfram.com/07.23.03.a9vn.01









  


  








Input Form





Hypergeometric2F1[-(19/4), 11/2, 3, z] == (2 Sqrt[2] (2 (1 - z)^(1/4) (-6688 - 160512 z + 9792432 z^2 - 58927100 z^3 + 128186409 z^4 - 118015326 z^5 + 39126945 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (-6688 - 160512 z + 9792432 z^2 - 58927100 z^3 + 128186409 z^4 - 118015326 z^5 + 39126945 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (-6688 - 160512 z + 9792432 z^2 - 58927100 z^3 + 128186409 z^4 - 118015326 z^5 + 39126945 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (-6688 - 160512 z + 9792432 z^2 - 58927100 z^3 + 128186409 z^4 - 118015326 z^5 + 39126945 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (-6688 - 160512 z + 9792432 z^2 - 58927100 z^3 + 128186409 z^4 - 118015326 z^5 + 39126945 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (-6688 - 157168 z + 1696608 z^2 + 8419624 z^3 - 68763929 z^4 + 145529163 z^5 - 125840715 z^6 + 39126945 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (8176707 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