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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=-23/4





http://functions.wolfram.com/07.23.03.8965.01









  


  










Input Form





Hypergeometric2F1[-(23/4), -(23/4), 6, -z] == (16384 Sqrt[2] ((-Sqrt[1 + z]) (9844736 + 278882912 z + 4350541701 z^2 + 55086258744 z^3 + 832926214428 z^4 - 28438540538520 z^5 + 101635952547822 z^6 - 111406812172344 z^7 + 42521633660604 z^8 - 5123141543752 z^9 + 126463255349 z^10) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (9844736 + 288727648 z + 4629424613 z^2 + 59436800445 z^3 + 888012473172 z^4 - 27605614324092 z^5 + 73197412009302 z^6 - 9770859624522 z^7 - 68885178511740 z^8 + 37398492116852 z^9 - 4996678288403 z^10 + 126463255349 z^11) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + Sqrt[1 + z] (9844736 + 278882912 z + 4350541701 z^2 + 55086258744 z^3 + 832926214428 z^4 - 28438540538520 z^5 + 101635952547822 z^6 - 111406812172344 z^7 + 42521633660604 z^8 - 5123141543752 z^9 + 126463255349 z^10) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (9844736 + 286266464 z + 4559011677 z^2 + 58329873327 z^3 + 873943807044 z^4 + 3654448540092 z^5 - 91206835501866 z^6 + 234852519844002 z^7 - 191507610888108 z^8 + 54759412216364 z^9 - 4829280913099 z^10 + 78718975335 z^11) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (257818892356660635 Pi z^5 Sqrt[1 + Sqrt[1 + z]])










Standard Form





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MathML Form







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<times /> <cn type='integer'> 27605614324092 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 888012473172 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 59436800445 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4629424613 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 288727648 </cn> <ci> z </ci> </apply> <cn type='integer'> 9844736 </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> 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<times /> <cn type='integer'> 101635952547822 </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'> 28438540538520 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 832926214428 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 55086258744 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4350541701 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 278882912 </cn> <ci> z </ci> </apply> <cn type='integer'> 9844736 </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> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 78718975335 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 11 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4829280913099 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 54759412216364 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 191507610888108 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 234852519844002 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 91206835501866 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3654448540092 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 873943807044 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 58329873327 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4559011677 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 286266464 </cn> <ci> z </ci> </apply> <cn 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02