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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=19/4, b>=a > For fixed z and a=19/4, b=19/4





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









  


  










Input Form





Hypergeometric2F1[19/4, 19/4, 7/2, z] == (1/(53361 Pi^(3/2) z^(5/2))) (2 ((4 Sqrt[z] (-5 + 45 z + 2997 z^2 + 1059 z^3) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^6 + (4 Sqrt[z] (-5 + 45 z + 2997 z^2 + 1059 z^3) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^6 - (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^5)) ((20 - 30 Sqrt[z] - 165 z + 255 z^(3/2) + 1230 z^2 + 4764 z^(5/2) + 963 z^3 + 1155 z^(7/2)) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^5 (1 + Sqrt[z])^6)) ((-20 - 30 Sqrt[z] + 165 z + 255 z^(3/2) - 1230 z^2 + 4764 z^(5/2) - 963 z^3 + 1155 z^(7/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)










Standard Form





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MathML Form







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type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <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'> 5 </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'> 6 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </cn> </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