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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=17/4, b>=a > For fixed z and a=17/4, b=21/4





http://functions.wolfram.com/07.23.03.an6u.01









  


  










Input Form





Hypergeometric2F1[17/4, 21/4, 5/2, z] == (1/(646425 Pi^(3/2) z^(3/2))) (4 ((2 (-3234 + 88935 z + 583447 z^2 + 309797 z^3 + 4095 z^4) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^7 - (2 (-3234 + 88935 z + 583447 z^2 + 309797 z^3 + 4095 z^4) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^7 - (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^6)) ((-3234 + 1617 Sqrt[z] + 87318 z + 118621 z^(3/2) + 464826 z^2 + 121427 z^(5/2) + 188370 z^3 + 4095 z^(7/2)) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^7)) ((3234 + 1617 Sqrt[z] - 87318 z + 118621 z^(3/2) - 464826 z^2 + 121427 z^(5/2) - 188370 z^3 + 4095 z^(7/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^2)










Standard Form





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MathML Form







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<power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 121427 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 464826 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 118621 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 87318 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 1617 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 3234 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 3 <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