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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.a7rd.01









  


  








Input Form





Hypergeometric2F1[-(23/4), 19/4, 5, -z] == (1/(192220753725 Pi z^4)) (4096 (1 + z)^(1/4) (4 (-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[1/2 - 1/(2 Sqrt[1 + 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) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] + Sqrt[1 + z] (55936 - 188784 z + 701385 z^2 - 4374370 z^3 + 18887505 z^4 + 208867932 z^5 + 517516272 z^6 + 576426240 z^7 + 308056320 z^8 + 64496640 z^9) EllipticK[1/2 - 1/(2 Sqrt[1 + z])]))








Standard Form





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MathML Form







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type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 701385 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 188784 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 55936 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </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