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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=17/4





http://functions.wolfram.com/07.23.03.9979.01









  


  










Input Form





Hypergeometric2F1[-(23/4), 17/4, 2, -z] == (8 Sqrt[2] (Sqrt[1 + z] (168245 + 27482253 z + 258021012 z^2 + 845258752 z^3 + 1260478464 z^4 + 880803840 z^5 + 234881024 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (168245 + 27650498 z + 285503265 z^2 + 1103279764 z^3 + 2105737216 z^4 + 2141282304 z^5 + 1115684864 z^6 + 234881024 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (168245 + 12844938 z + 97306653 z^2 + 276123712 z^3 + 369481728 z^4 + 236716032 z^5 + 58720256 z^6) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - Sqrt[1 + z] (168245 + 27482253 z + 258021012 z^2 + 845258752 z^3 + 1260478464 z^4 + 880803840 z^5 + 234881024 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (59053995 Pi z Sqrt[1 + Sqrt[1 + z]])










Standard Form





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MathML Form







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<cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 27482253 </cn> <ci> z </ci> </apply> <cn type='integer'> 168245 </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