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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/07.23.03.9039.01









  


  










Input Form





Hypergeometric2F1[-(23/4), -(19/4), 4, -z] == (256 Sqrt[2] ((-Sqrt[1 + z]) (6688 + 223003 z + 5806647 z^2 - 297277069 z^3 + 1290416567 z^4 - 1505188359 z^5 + 523880605 z^6 - 43596935 z^7 + 174933 z^8) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - (6688 + 229691 z + 6029650 z^2 - 291470422 z^3 + 993139498 z^4 - 214771792 z^5 - 981307754 z^6 + 480283670 z^7 - 43422002 z^8 + 174933 z^9) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + Sqrt[1 + z] (6688 + 223003 z + 5806647 z^2 - 297277069 z^3 + 1290416567 z^4 - 1505188359 z^5 + 523880605 z^6 - 43596935 z^7 + 174933 z^8) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - (-6688 - 228019 z - 5973429 z^2 - 14008367 z^3 + 1009623415 z^4 - 3079682553 z^5 + 2564616161 z^6 - 634909669 z^7 + 35161533 z^8) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (39289077135 Pi z^3 Sqrt[1 + Sqrt[1 + z]])










Standard Form





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MathML Form







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<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'> 35161533 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 634909669 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2564616161 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3079682553 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1009623415 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 14008367 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5973429 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 228019 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -6688 </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'> 39289077135 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </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