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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.abz3.01









  


  








Input Form





Hypergeometric2F1[-(7/2), -(3/4), 6, z] == (32 Sqrt[2] (2 (1 - z)^(1/4) (32768 - 388096 z + 2235200 z^2 - 8858592 z^3 + 33411360 z^4 + 149882752 z^5 + 20900836 z^6 - 1682450 z^7 + 100947 z^8) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (32768 - 388096 z + 2235200 z^2 - 8858592 z^3 + 33411360 z^4 + 149882752 z^5 + 20900836 z^6 - 1682450 z^7 + 100947 z^8) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (32768 - 404480 z + 2426176 z^2 - 9941344 z^3 + 37648320 z^4 - 96150848 z^5 - 128711740 z^6 - 567226 z^7 + 33649 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (32768 - 388096 z + 2235200 z^2 - 8858592 z^3 + 33411360 z^4 + 149882752 z^5 + 20900836 z^6 - 1682450 z^7 + 100947 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (32768 - 388096 z + 2235200 z^2 - 8858592 z^3 + 33411360 z^4 + 149882752 z^5 + 20900836 z^6 - 1682450 z^7 + 100947 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (32768 - 388096 z + 2235200 z^2 - 8858592 z^3 + 33411360 z^4 + 149882752 z^5 + 20900836 z^6 - 1682450 z^7 + 100947 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (3681032355 Pi Sqrt[1 + Sqrt[1 - z]] z^5)








Standard Form





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MathML Form







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</apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 100947 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1682450 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 20900836 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 149882752 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 33411360 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> 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z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 33411360 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8858592 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2235200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 388096 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 32768 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <plus /> <apply> <power 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02