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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/07.23.03.9479.01









  


  








Input Form





Hypergeometric2F1[-(23/4), 1/4, 4, -z] == (256 Sqrt[2] (Sqrt[1 + z] (-13984 - 160379 z - 1052296 z^2 + 2665558 z^3 + 1644692 z^4 + 885997 z^5 + 336476 z^6 + 77824 z^7 + 8192 z^8) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (-13984 - 174363 z - 1212675 z^2 + 1613262 z^3 + 4310250 z^4 + 2530689 z^5 + 1222473 z^6 + 414300 z^7 + 86016 z^8 + 8192 z^9) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-13984 - 170867 z - 1171597 z^2 - 5813990 z^3 + 464030 z^4 + 242809 z^5 + 89327 z^6 + 20032 z^7 + 2048 z^8) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-13984 - 160379 z - 1052296 z^2 + 2665558 z^3 + 1644692 z^4 + 885997 z^5 + 336476 z^6 + 77824 z^7 + 8192 z^8) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (985747455 Pi z^3 Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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<times /> <cn type='integer'> 170867 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -13984 </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'> 8192 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 77824 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 336476 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 885997 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1644692 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2665558 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1052296 </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'> 160379 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -13984 </cn> </apply> <apply> <ci> EllipticK 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</semantics> </math>










Rule Form





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





2007-05-02