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BesselY




Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselY[nu,z] > Differential equations > Ordinary linear differential equations and wronskians > For the direct function itself





http://functions.wolfram.com/03.03.13.0003.01









  


  








Input Form





Derivative[2][w][z] + a z^n w[z] == 0 /; w[z] == Sqrt[z] (Subscript[c, 1] BesselJ[1/(n + 2), ((2 Sqrt[a])/(n + 2)) z^((n + 2)/2)] + Subscript[c, 2] BesselY[1/(n + 2), ((2 Sqrt[a])/(n + 2)) z^((n + 2)/2)])








Standard Form





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MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mrow> <msup> <mi> w </mi> <mi> &#8242;&#8242; </mi> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> n </mi> </msup> </mrow> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mtext> </mtext> <mrow> <mrow> <msub> <mi> c </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <mrow> <msub> <mi> J </mi> <mfrac> <mn> 1 </mn> <mrow> <mi> n </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </mfrac> </msub> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mrow> <mi> n </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </mfrac> <mo> &#8290; </mo> <msup> <mi> z </mi> <mfrac> <mrow> <mi> n </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mn> 2 </mn> </mfrac> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mtext> </mtext> <mrow> <msub> <mi> c </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mrow> <msub> <mi> Y </mi> <mfrac> <mn> 1 </mn> <mrow> <mi> n </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </mfrac> </msub> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mrow> <mi> n </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </mfrac> <mo> &#8290; </mo> <msup> <mi> z </mi> <mfrac> <mrow> <mi> n </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mn> 2 </mn> </mfrac> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <plus /> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <ci> w </ci> <ci> z </ci> </apply> <apply> <power /> <ci> z </ci> <ci> n </ci> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <eq /> <apply> <ci> w </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> c </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> BesselJ </ci> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <apply> <plus /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> BesselY </ci> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <apply> <plus /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </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)





2001-10-29