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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=-21/4, b>=a > For fixed z and a=-21/4, b=-21/4





http://functions.wolfram.com/07.23.03.a85c.01









  


  










Input Form





Hypergeometric2F1[-(21/4), -(21/4), 4, -z] == (256 Sqrt[2] ((-(148512 + 5044767 z + 132514473 z^2 - 17515159157 z^3 + 101646046925 z^4 - 159595913027 z^5 + 80792529403 z^6 - 12110237863 z^7 + 343516207 z^8)) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (148512 + 5044767 z + 132514473 z^2 - 17515159157 z^3 + 101646046925 z^4 - 159595913027 z^5 + 80792529403 z^6 - 12110237863 z^7 + 343516207 z^8) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + Sqrt[1 + z] (148512 + 5007639 z + 131279967 z^2 - 10629344585 z^3 + 55351524775 z^4 - 78978387267 z^5 + 36096854341 z^6 - 4771942667 z^7 + 111035925 z^8) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + (148512 + 5044767 z + 132514473 z^2 - 17515159157 z^3 + 101646046925 z^4 - 159595913027 z^5 + 80792529403 z^6 - 12110237863 z^7 + 343516207 z^8) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (885511501875 Pi z^3 Sqrt[1 + Sqrt[1 + z]])










Standard Form





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MathML Form







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type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 343516207 </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'> 12110237863 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 80792529403 </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'> 159595913027 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 101646046925 </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'> 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Rule Form





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





2007-05-02