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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=1/4





http://functions.wolfram.com/07.23.03.9487.01









  


  










Input Form





Hypergeometric2F1[-(23/4), 1/4, 6, -z] == (16384 Sqrt[2] (Sqrt[1 + z] (-47104 - 574816 z - 3346293 z^2 - 12875929 z^3 - 42935158 z^4 + 54940494 z^5 + 23552431 z^6 + 9241723 z^7 + 2664204 z^8 + 483328 z^9 + 40960 z^10) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (-47104 - 621920 z - 3921109 z^2 - 16222222 z^3 - 55811087 z^4 + 12005336 z^5 + 78492925 z^6 + 32794154 z^7 + 11905927 z^8 + 3147532 z^9 + 524288 z^10 + 40960 z^11) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-47104 - 610144 z - 3774093 z^2 - 15346750 z^3 - 52374427 z^4 - 178247076 z^5 + 6460909 z^6 + 2482978 z^7 + 698715 z^8 + 123712 z^9 + 10240 z^10) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-47104 - 574816 z - 3346293 z^2 - 12875929 z^3 - 42935158 z^4 + 54940494 z^5 + 23552431 z^6 + 9241723 z^7 + 2664204 z^8 + 483328 z^9 + 40960 z^10) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (1653098482035 Pi z^5 Sqrt[1 + Sqrt[1 + z]])










Standard Form





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MathML Form







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type='integer'> -47104 </cn> </apply> <apply> <ci> EllipticE </ci> <apply> <times /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </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> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 10240 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 123712 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 698715 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> 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Rule Form





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





2007-05-02