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HypergeometricU




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricU[a,b,z] > Specific values > For fixed z > For fixed z and a=11/2





http://functions.wolfram.com/07.33.03.0791.01









  


  








Input Form





HypergeometricU[11/2, -4, -z] == -((1/(618718975875 Sqrt[Pi])) ((128 z (z (-22680 + z (-42525 + 8 z (-6615 + z (-178605 + 2 z (99225 + z (-35457 + 4 z (1335 + z (-87 + 2 z)))))))) BesselK[0, z/2] + (-90720 + z (-170100 + z (-214515 + 8 z (-33075 + z (-59535 + 2 z (70797 + z (-30615 + 4 z (1251 + z (-85 + 2 z))))))))) BesselK[1, z/2] - (z (-22680 + z (-42525 + 8 z (-6615 + z (-178605 + 2 z (99225 + z (-35457 + 4 z (1335 + z (-87 + 2 z)))))))) BesselI[0, z/2] + (90720 + z (170100 + z (214515 - 8 z (-33075 + z (-59535 + 2 z (70797 + z (-30615 + 4 z (1251 + z (-85 + 2 z))))))))) BesselI[1, z/2]) (Log[-z] - Log[z])))/E^(z/2)))








Standard Form





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MathML Form







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</apply> <cn type='integer'> -35457 </cn> </apply> </apply> <cn type='integer'> 99225 </cn> </apply> </apply> <cn type='integer'> -178605 </cn> </apply> </apply> <cn type='integer'> -6615 </cn> </apply> </apply> <cn type='integer'> -42525 </cn> </apply> </apply> <cn type='integer'> -22680 </cn> </apply> <apply> <ci> BesselI </ci> <cn type='integer'> 0 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <cn type='integer'> 214515 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> -85 </cn> </apply> </apply> <cn type='integer'> 1251 </cn> </apply> </apply> <cn type='integer'> -30615 </cn> </apply> </apply> <cn type='integer'> 70797 </cn> </apply> </apply> <cn type='integer'> -59535 </cn> </apply> </apply> <cn type='integer'> -33075 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 170100 </cn> </apply> </apply> <cn type='integer'> 90720 </cn> </apply> <apply> <ci> BesselI </ci> <cn type='integer'> 1 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <ln /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <ci> z </ci> </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