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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=-7/4, b>=a > For fixed z and a=-7/4, b=1/2





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









  


  










Input Form





Hypergeometric2F1[-(7/4), 1/2, 5, z] == (256 Sqrt[2] (-2 (1 - z)^(1/4) (384 - 2432 z + 6776 z^2 - 12033 z^3 - 3040 z^4 + 400 z^5) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] - 2 (1 - z)^(3/4) (384 - 2432 z + 6776 z^2 - 12033 z^3 - 3040 z^4 + 400 z^5) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] + (1 - z)^(1/4) (384 - 2432 z + 6776 z^2 - 12033 z^3 - 3040 z^4 + 400 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] + Sqrt[1 - z] (384 - 2432 z + 6776 z^2 - 12033 z^3 - 3040 z^4 + 400 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (384 - 2432 z + 6776 z^2 - 12033 z^3 - 3040 z^4 + 400 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (384 - 2624 z + 7956 z^2 - 15211 z^3 + 22160 z^4 - 3120 z^5 + 400 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (2523675 Pi Sqrt[1 + Sqrt[1 - z]] z^4)










Standard Form





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MathML Form







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<apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3040 </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'> 12033 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 6776 </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'> 2432 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 384 </cn> </apply> <apply> <ci> EllipticE </ci> <apply> <times /> <apply> <plus /> <apply> 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type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <plus /> <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> <cn type='integer'> -1 </cn> </apply> </apply> <ci> z </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </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'> 3 <sep /> 4 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3040 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> 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Rule Form





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





2007-05-02