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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/07.23.03.9717.01









  


  








Input Form





Hypergeometric2F1[-(23/4), 9/4, 1, -z] == (1/(504735 Pi Sqrt[1 + Sqrt[1 + z]])) (2 Sqrt[2] (4 Sqrt[1 + z] (243519 + 2319537 z + 6884688 z^2 + 9158272 z^3 + 5726208 z^4 + 1376256 z^5) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + 4 (243519 + 2563056 z + 9204225 z^2 + 16042960 z^3 + 14884480 z^4 + 7102464 z^5 + 1376256 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 4 Sqrt[1 + z] (243519 + 2319537 z + 6884688 z^2 + 9158272 z^3 + 5726208 z^4 + 1376256 z^5) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - (469341 + 3447150 z + 8829345 z^2 + 10591360 z^3 + 6113280 z^4 + 1376256 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))








Standard Form





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MathML Form







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</apply> <apply> <times /> <cn type='integer'> 8829345 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3447150 </cn> <ci> z </ci> </apply> <cn type='integer'> 469341 </cn> </apply> <apply> <ci> EllipticK </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> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02