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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=-23/4, b>=a > For fixed z and a=-23/4, b=7/2





http://functions.wolfram.com/07.23.03.9880.01









  


  








Input Form





Hypergeometric2F1[-(23/4), 7/2, 4, z] == (32 Sqrt[2] (-2 (1 - z)^(1/4) (153824 + 394174 z + 2119887 z^2 - 44842880 z^3 + 155802485 z^4 - 246890490 z^5 + 206918985 z^6 - 89597820 z^7 + 15862275 z^8) EllipticE[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (153824 + 394174 z + 2119887 z^2 - 44842880 z^3 + 155802485 z^4 - 246890490 z^5 + 206918985 z^6 - 89597820 z^7 + 15862275 z^8) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] + (1 - z)^(1/4) (153824 + 394174 z + 2119887 z^2 - 44842880 z^3 + 155802485 z^4 - 246890490 z^5 + 206918985 z^6 - 89597820 z^7 + 15862275 z^8) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (153824 + 394174 z + 2119887 z^2 - 44842880 z^3 + 155802485 z^4 - 246890490 z^5 + 206918985 z^6 - 89597820 z^7 + 15862275 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] + (1 - z)^(3/4) (153824 + 394174 z + 2119887 z^2 - 44842880 z^3 + 155802485 z^4 - 246890490 z^5 + 206918985 z^6 - 89597820 z^7 + 15862275 z^8) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (153824 + 317262 z + 1908379 z^2 - 1940405 z^3 - 48906825 z^4 + 178342835 z^5 - 275188095 z^6 + 222300585 z^7 - 92770275 z^8 + 15862275 z^9) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)]))/(704105325 Pi Sqrt[1 + Sqrt[1 - z]] z^3)








Standard Form





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MathML Form







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<cn type='rational'> 3 <sep /> 4 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 15862275 </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'> 89597820 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 206918985 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 246890490 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 155802485 </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'> 44842880 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> 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/> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <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 /> 4 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 15862275 </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'> 89597820 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 206918985 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 246890490 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> 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</semantics> </math>










Rule Form





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





2007-05-02