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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.a7rc.01









  


  








Input Form





Hypergeometric2F1[-(23/4), 19/4, 5, z] == -((1/(192220753725 Pi z^4)) (4096 Sqrt[1 + Sqrt[z]] (2 (27968 + 73416 z + 276621 z^2 + 1911875 z^3 - 39171405 z^4 + 141625029 z^5 - 232438752 z^6 + 200657808 z^7 - 89107200 z^8 + 16124160 z^9) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-55936 + 55936 Sqrt[z] - 188784 z + 188784 z^(3/2) - 701385 z^2 + 701385 z^(5/2) - 4374370 z^3 + 4374370 z^(7/2) - 18887505 z^4 + 18887505 z^(9/2) + 208867932 z^5 - 208867932 z^(11/2) - 517516272 z^6 + 517516272 z^(13/2) + 576426240 z^7 - 576426240 z^(15/2) - 308056320 z^8 + 308056320 z^(17/2) + 64496640 z^9 - 64496640 z^(19/2)) EllipticK[ (2 Sqrt[z])/(1 + Sqrt[z])])))








Standard Form





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MathML Form







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type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -55936 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <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