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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=-9/2, b>=a > For fixed z and a=-9/2, b=-11/4





http://functions.wolfram.com/07.23.03.a9z7.01









  


  








Input Form





Hypergeometric2F1[-(9/2), -(11/4), 4, z] == (Sqrt[2] (-2 (1 - z)^(1/4) (-21504 + 455616 z - 6989472 z^2 - 199896640 z^3 - 382027200 z^4 - 136296756 z^5 - 4508966 z^6 + 100947 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (-21504 + 455616 z - 6989472 z^2 - 199896640 z^3 - 382027200 z^4 - 136296756 z^5 - 4508966 z^6 + 100947 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-21504 + 466368 z - 7215264 z^2 + 403040 z^3 + 302944160 z^4 + 362198124 z^5 + 70375402 z^6 + 33649 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (-21504 + 455616 z - 6989472 z^2 - 199896640 z^3 - 382027200 z^4 - 136296756 z^5 - 4508966 z^6 + 100947 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (-21504 + 455616 z - 6989472 z^2 - 199896640 z^3 - 382027200 z^4 - 136296756 z^5 - 4508966 z^6 + 100947 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (-21504 + 455616 z - 6989472 z^2 - 199896640 z^3 - 382027200 z^4 - 136296756 z^5 - 4508966 z^6 + 100947 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (98423325 Pi Sqrt[1 + Sqrt[1 - z]] z^3)








Standard Form





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MathML Form







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type='integer'> 4508966 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 136296756 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 382027200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 199896640 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6989472 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 455616 </cn> <ci> z </ci> </apply> <cn type='integer'> -21504 </cn> </apply> <apply> <ci> EllipticK 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Date Added to functions.wolfram.com (modification date)





2007-05-02