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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=11/4





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









  


  










Input Form





Hypergeometric2F1[-(17/4), 11/4, 11/2, z] == (1/(65716497 Pi^(3/2) z^(9/2))) (8 (2 Sqrt[z] (-26520 + 106080 z - 97461 z^2 - 78897 z^3 + 1837689 z^4 - 3420123 z^5 + 2860928 z^6 - 1181696 z^7 + 196608 z^8) EllipticE[(1/2) (1 - Sqrt[z])] + 2 Sqrt[z] (-26520 + 106080 z - 97461 z^2 - 78897 z^3 + 1837689 z^4 - 3420123 z^5 + 2860928 z^6 - 1181696 z^7 + 196608 z^8) EllipticE[(1/2) (1 + Sqrt[z])] - (53040 - 26520 Sqrt[z] - 251940 z + 106080 z^(3/2) + 348075 z^2 - 97461 z^(5/2) + 32487 z^3 - 78897 z^(7/2) + 301665 z^4 + 1837689 z^(9/2) - 693903 z^5 - 3420123 z^(11/2) + 639632 z^6 + 2860928 z^(13/2) - 281600 z^7 - 1181696 z^(15/2) + 49152 z^8 + 196608 z^(17/2)) EllipticK[(1/2) (1 - Sqrt[z])] - (-53040 - 26520 Sqrt[z] + 251940 z + 106080 z^(3/2) - 348075 z^2 - 97461 z^(5/2) - 32487 z^3 - 78897 z^(7/2) - 301665 z^4 + 1837689 z^(9/2) + 693903 z^5 - 3420123 z^(11/2) - 639632 z^6 + 2860928 z^(13/2) + 281600 z^7 - 1181696 z^(15/2) - 49152 z^8 + 196608 z^(17/2)) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[1/4]^2)










Standard Form





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MathML Form







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</apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1181696 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2860928 </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'> 3420123 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1837689 </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'> 78897 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 97461 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 106080 </cn> <ci> z </ci> </apply> <cn type='integer'> -26520 </cn> </apply> <apply> <ci> EllipticE </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 196608 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1181696 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2860928 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> 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type='integer'> 1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 196608 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 17 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 49152 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1181696 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 281600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2860928 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 639632 </cn> <apply> <power /> 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type='rational'> 13 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 639632 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3420123 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 693903 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1837689 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 301665 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 78897 </cn> <apply> <power 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Rule Form





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





2007-05-02