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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=-11/2, b>=a > For fixed z and a=-11/2, b=-21/4





http://functions.wolfram.com/07.23.03.a7w8.01









  


  










Input Form





Hypergeometric2F1[-(11/2), -(21/4), 5, z] == (4 Sqrt[2] (2 (-172032 + 5017600 z - 87721984 z^2 + 1590441216 z^3 + 124616679680 z^4 + 578386451296 z^5 + 769061327040 z^6 + 343525885432 z^7 + 47295395672 z^8 + 1313692695 z^9) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (-172032 + 5017600 z - 87721984 z^2 + 1590441216 z^3 + 124616679680 z^4 + 578386451296 z^5 + 769061327040 z^6 + 343525885432 z^7 + 47295395672 z^8 + 1313692695 z^9) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (-172032 + 4931584 z - 85283072 z^2 + 1548556800 z^3 + 60329463680 z^4 + 225000288416 z^5 + 242144164848 z^6 + 84517648696 z^7 + 8318238460 z^8 + 124494825 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (-172032 + 5017600 z - 87721984 z^2 + 1590441216 z^3 + 124616679680 z^4 + 578386451296 z^5 + 769061327040 z^6 + 343525885432 z^7 + 47295395672 z^8 + 1313692695 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (-172032 + 5017600 z - 87721984 z^2 + 1590441216 z^3 + 124616679680 z^4 + 578386451296 z^5 + 769061327040 z^6 + 343525885432 z^7 + 47295395672 z^8 + 1313692695 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (-172032 + 5017600 z - 87721984 z^2 + 1590441216 z^3 + 124616679680 z^4 + 578386451296 z^5 + 769061327040 z^6 + 343525885432 z^7 + 47295395672 z^8 + 1313692695 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (130097092125 Pi Sqrt[1 + Sqrt[1 - z]] z^4)










Standard Form





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MathML Form







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type='integer'> -172032 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <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 /> 4 </cn> </apply> <apply> <power /> <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> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </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 /> 4 </cn> </apply> <apply> <plus 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<apply> <plus /> <apply> <times /> <cn type='integer'> 1313692695 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 47295395672 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 343525885432 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 769061327040 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 578386451296 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 124616679680 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1590441216 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> 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Rule Form





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





2007-05-02