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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=-7/2, b>=a > For fixed z and a=-7/2, b=-3/4





http://functions.wolfram.com/07.23.03.abz2.01









  


  








Input Form





Hypergeometric2F1[-(7/2), -(3/4), 5, z] == (16 Sqrt[2] (2 (1 - z)^(1/4) (-2048 + 23552 z - 139584 z^2 + 697200 z^3 + 4076080 z^4 + 692208 z^5 - 64372 z^6 + 4389 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (-2048 + 23552 z - 139584 z^2 + 697200 z^3 + 4076080 z^4 + 692208 z^5 - 64372 z^6 + 4389 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (-2048 + 24576 z - 151168 z^2 + 764880 z^3 - 2144480 z^4 - 3758912 z^5 - 21736 z^6 + 1463 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (-2048 + 23552 z - 139584 z^2 + 697200 z^3 + 4076080 z^4 + 692208 z^5 - 64372 z^6 + 4389 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (-2048 + 23552 z - 139584 z^2 + 697200 z^3 + 4076080 z^4 + 692208 z^5 - 64372 z^6 + 4389 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (-2048 + 23552 z - 139584 z^2 + 697200 z^3 + 4076080 z^4 + 692208 z^5 - 64372 z^6 + 4389 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (47072025 Pi Sqrt[1 + Sqrt[1 - z]] z^4)








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