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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=21/4





http://functions.wolfram.com/07.23.03.a9uj.01









  


  










Input Form





Hypergeometric2F1[-(19/4), 21/4, -(3/2), z] == (1/(13260 Pi^(3/2))) ((-((1/(-1 + z)^2) (4 Sqrt[z] (-3315 - 49725 z + 26487306 z^2 - 170640384 z^3 + 379072512 z^4 - 352321536 z^5 + 117440512 z^6) EllipticE[(1/2) (1 - Sqrt[z])])) + (1/(-1 + z)^2) (4 Sqrt[z] (-3315 - 49725 z + 26487306 z^2 - 170640384 z^3 + 379072512 z^4 - 352321536 z^5 + 117440512 z^6) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^2 (1 + Sqrt[z]))) ((13260 - 19890 Sqrt[z] + 208845 z - 308295 z^(3/2) + 4972500 z^2 + 48002112 z^(5/2) - 100909056 z^3 - 240371712 z^(7/2) + 389308416 z^4 + 368836608 z^(9/2) - 528482304 z^5 - 176160768 z^(11/2) + 234881024 z^6) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/(-1 - Sqrt[z] + z + z^(3/2))) ((13260 + 19890 Sqrt[z] + 208845 z + 308295 z^(3/2) + 4972500 z^2 - 48002112 z^(5/2) - 100909056 z^3 + 240371712 z^(7/2) + 389308416 z^4 - 368836608 z^(9/2) - 528482304 z^5 + 176160768 z^(11/2) + 234881024 z^6) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^2)










Standard Form





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MathML Form







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type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 117440512 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 352321536 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 379072512 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 170640384 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 26487306 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> 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<ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 176160768 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 528482304 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 368836608 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 389308416 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 240371712 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02