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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=-15/4, b>=a > For fixed z and a=-15/4, b=13/4





http://functions.wolfram.com/07.23.03.abm6.01









  


  








Input Form





Hypergeometric2F1[-(15/4), 13/4, 3, -z] == (64 Sqrt[2] (Sqrt[1 + z] (-308 + 2387 z + 72907 z^2 + 203392 z^3 + 198656 z^4 + 65536 z^5) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + (-308 + 2079 z + 75294 z^2 + 276299 z^3 + 402048 z^4 + 264192 z^5 + 65536 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 4 (-77 + 539 z + 6850 z^2 + 15676 z^3 + 13568 z^4 + 4096 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-308 + 2387 z + 72907 z^2 + 203392 z^3 + 198656 z^4 + 65536 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (1514205 Pi z^2 Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2387 </cn> <ci> z </ci> </apply> <cn type='integer'> -308 </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> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02