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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=9/4





http://functions.wolfram.com/07.23.03.9725.01









  


  










Input Form





Hypergeometric2F1[-(23/4), 9/4, 3, -z] == (64 Sqrt[2] (2 Sqrt[1 + z] (-67298 + 168245 z + 3318912 z^2 + 10595225 z^3 + 15838816 z^4 + 12715776 z^5 + 5324800 z^6 + 917504 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + 2 (-67298 + 100947 z + 3487157 z^2 + 13914137 z^3 + 26434041 z^4 + 28554592 z^5 + 18040576 z^6 + 6242304 z^7 + 917504 z^8) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-134596 + 235543 z + 2498997 z^2 + 6887941 z^3 + 9400043 z^4 + 7047552 z^5 + 2791424 z^6 + 458752 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 2 Sqrt[1 + z] (-67298 + 168245 z + 3318912 z^2 + 10595225 z^3 + 15838816 z^4 + 12715776 z^5 + 5324800 z^6 + 917504 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (140821065 Pi z^2 Sqrt[1 + Sqrt[1 + z]])










Standard Form





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MathML Form







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</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> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 140821065 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </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='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02