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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=5/4





http://functions.wolfram.com/07.23.03.9611.01









  


  










Input Form





Hypergeometric2F1[-(23/4), 5/4, 6, -z] == (16384 Sqrt[2] (Sqrt[1 + z] (894976 + 8516256 z + 35618559 z^2 + 83754109 z^3 + 105994350 z^4 + 182133714 z^5 + 172481939 z^6 + 105871761 z^7 + 41629056 z^8 + 9574400 z^9 + 983040 z^10) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (894976 + 9411232 z + 44134815 z^2 + 119372668 z^3 + 189748459 z^4 + 288128064 z^5 + 354615653 z^6 + 278353700 z^7 + 147500817 z^8 + 51203456 z^9 + 10557440 z^10 + 983040 z^11) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (894976 + 9187488 z + 41942823 z^2 + 109898071 z^3 + 166562550 z^4 + 54940494 z^5 + 49396067 z^6 + 29105547 z^7 + 11048784 z^8 + 2462720 z^9 + 245760 z^10) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - Sqrt[1 + z] (894976 + 8516256 z + 35618559 z^2 + 83754109 z^3 + 105994350 z^4 + 182133714 z^5 + 172481939 z^6 + 105871761 z^7 + 41629056 z^8 + 9574400 z^9 + 983040 z^10) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (1653098482035 Pi z^5 Sqrt[1 + Sqrt[1 + z]])










Standard Form





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MathML Form







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<cn type='integer'> 288128064 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 189748459 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 119372668 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 44134815 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 9411232 </cn> <ci> z </ci> </apply> <cn type='integer'> 894976 </cn> </apply> <apply> <ci> EllipticE </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> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 245760 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2462720 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 11048784 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 29105547 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 49396067 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 54940494 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 166562550 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 109898071 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 41942823 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 9187488 </cn> <ci> z </ci> </apply> <cn type='integer'> 894976 </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> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 983040 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 9574400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 41629056 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 105871761 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 172481939 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 182133714 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> 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</apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 1653098482035 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </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