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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/07.23.03.9467.01









  


  








Input Form





Hypergeometric2F1[-(23/4), 1/4, 1, -z] == (1/(504735 Pi Sqrt[1 + Sqrt[1 + z]])) (2 Sqrt[2] (2 Sqrt[1 + z] (184197 + 350448 z + 432849 z^2 + 314582 z^3 + 123904 z^4 + 20480 z^5) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + 2 (184197 + 534645 z + 783297 z^2 + 747431 z^3 + 438486 z^4 + 144384 z^5 + 20480 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-136341 + 220089 z + 253473 z^2 + 173395 z^3 + 64832 z^4 + 10240 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 2 Sqrt[1 + z] (184197 + 350448 z + 432849 z^2 + 314582 z^3 + 123904 z^4 + 20480 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))








Standard Form





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MathML Form







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<power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 350448 </cn> <ci> z </ci> </apply> <cn type='integer'> 184197 </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