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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=21/4





http://functions.wolfram.com/07.23.03.a7sz.01









  


  










Input Form





Hypergeometric2F1[-(23/4), 21/4, 3, -z] == (64 Sqrt[2] (Sqrt[1 + z] (-672980 + 17329235 z + 1742443467 z^2 + 13523709344 z^3 + 39683983360 z^4 + 55072260096 z^5 + 36582719488 z^6 + 9395240960 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (-672980 + 16656255 z + 1759772702 z^2 + 15266152811 z^3 + 53207692704 z^4 + 94756243456 z^5 + 91654979584 z^6 + 45977960448 z^7 + 9395240960 z^8) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 4 (-168245 + 4206125 z + 195735558 z^2 + 1245569702 z^3 + 3199251328 z^4 + 4009377792 z^5 + 2451570688 z^6 + 587202560 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-672980 + 17329235 z + 1742443467 z^2 + 13523709344 z^3 + 39683983360 z^4 + 55072260096 z^5 + 36582719488 z^6 + 9395240960 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (31121455365 Pi z^2 Sqrt[1 + Sqrt[1 + z]])










Standard Form





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MathML Form







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<cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 36582719488 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 55072260096 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 39683983360 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 13523709344 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1742443467 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 17329235 </cn> <ci> z </ci> </apply> <cn type='integer'> -672980 </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> <power /> <apply> <times /> <cn type='integer'> 31121455365 </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