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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=-19/4





http://functions.wolfram.com/07.23.03.9027.01









  


  










Input Form





Hypergeometric2F1[-(23/4), -(19/4), 1, -z] == (1/(168245 Pi Sqrt[1 + Sqrt[1 + z]])) (2 Sqrt[2] (Sqrt[1 + z] (238281 - 3887071 z + 11003162 z^2 - 7535774 z^3 + 1090317 z^4 - 7315 z^5) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + (238281 - 3648790 z + 7116091 z^2 + 3467388 z^3 - 6445457 z^4 + 1083002 z^5 - 7315 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + Sqrt[1 + z] (-238281 + 3887071 z - 11003162 z^2 + 7535774 z^3 - 1090317 z^4 + 7315 z^5) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - 4 (17509 + 219079 z - 3025302 z^2 + 5767430 z^3 - 2645263 z^4 + 241395 z^5) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])]))










Standard Form





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MathML Form







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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