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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/07.23.03.9471.01









  


  










Input Form





Hypergeometric2F1[-(23/4), 1/4, 2, -z] == (8 Sqrt[2] (Sqrt[1 + z] (-168245 + 1729557 z + 1926405 z^2 + 1659911 z^3 + 924300 z^4 + 294912 z^5 + 40960 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (-168245 + 1561312 z + 3655962 z^2 + 3586316 z^3 + 2584211 z^4 + 1219212 z^5 + 335872 z^6 + 40960 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-168245 - 1803588 z + 573714 z^2 + 471260 z^3 + 250491 z^4 + 76608 z^5 + 10240 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-168245 + 1729557 z + 1926405 z^2 + 1659911 z^3 + 924300 z^4 + 294912 z^5 + 40960 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (13627845 Pi z Sqrt[1 + Sqrt[1 + z]])










Standard Form





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MathML Form







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<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