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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=6





http://functions.wolfram.com/07.33.03.0839.01









  


  










Input Form





HypergeometricU[6, -(7/2), z] == (1/9820936125) (8 (12600 + z (-21600 + z (30240 + z (-53760 + z (241920 + z (274845 + 4 z (22745 + 2 z (1569 + 2 z (47 + z))))))))) - 4 E^z Sqrt[Pi] z^(9/2) (692835 + 2 z (314925 + 4 z (24225 + 2 z (1615 + z (95 + 2 z))))) Erfc[Sqrt[z]])










Standard Form





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MathML Form







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</mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 47 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1569 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 22745 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 274845 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 241920 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 53760 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 30240 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 21600 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 12600 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mi> z </mi> </msup> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 95 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1615 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 24225 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 314925 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 692835 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> erfc </mi> <mo> &#8289; </mo> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricU </ci> <cn type='integer'> 6 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 9820936125 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <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 /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 47 </cn> </apply> </apply> <cn type='integer'> 1569 </cn> </apply> </apply> <cn type='integer'> 22745 </cn> </apply> </apply> <cn type='integer'> 274845 </cn> </apply> </apply> <cn type='integer'> 241920 </cn> </apply> </apply> <cn type='integer'> -53760 </cn> </apply> </apply> <cn type='integer'> 30240 </cn> </apply> </apply> <cn type='integer'> -21600 </cn> </apply> </apply> <cn type='integer'> 12600 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <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'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> 95 </cn> </apply> </apply> <cn type='integer'> 1615 </cn> </apply> </apply> <cn type='integer'> 24225 </cn> </apply> </apply> <cn type='integer'> 314925 </cn> </apply> </apply> <cn type='integer'> 692835 </cn> </apply> <apply> <ci> Erfc </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </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