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variants of this functions
KelvinKei






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/03.19.13.0009.01









  


  










Input Form





Derivative[4][w][z] - 4 (Log[r] + Log[s]) Derivative[3][w][z] + 2 ((-(-2 + \[Nu]^2)) Log[r]^2 + 6 Log[r] Log[s] + 3 Log[s]^2) Derivative[2][w][z] + 4 (Log[r] + Log[s]) (\[Nu]^2 Log[r]^2 - 2 Log[r] Log[s] - Log[s]^2) Derivative[1][w][z] + ((a^4 r^(4 z) - 4 \[Nu]^2 + \[Nu]^4) Log[r]^4 - 4 \[Nu]^2 Log[r]^3 Log[s] - 2 (-2 + \[Nu]^2) Log[r]^2 Log[s]^2 + 4 Log[r] Log[s]^3 + Log[s]^4) w[z] == 0 /; w[z] == Subscript[c, 1] s^z KelvinBer[\[Nu], a r^z] + Subscript[c, 2] s^z KelvinBei[\[Nu], a r^z] + Subscript[c, 3] s^z KelvinKer[\[Nu], a r^z] + Subscript[c, 4] s^z KelvinKei[\[Nu], a r^z]










Standard Form





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MathML Form







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</mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mtext> </mtext> </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'> 4 </cn> </degree> </bvar> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <ln /> <ci> r </ci> </apply> <apply> <ln /> <ci> s </ci> </apply> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 3 </cn> </degree> </bvar> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <plus /> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -2 </cn> </apply> </apply> <apply> <power /> <apply> <ln /> <ci> r </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <ln /> <ci> s </ci> </apply> <apply> <ln /> <ci> r </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <apply> <ln /> <ci> s </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <ln /> <ci> r </ci> </apply> <apply> <ln /> <ci> s </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> &#957; 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</ci> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> s </ci> <ci> z </ci> </apply> <apply> <ci> KelvinBei </ci> <ci> &#957; </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> c </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <ci> s </ci> <ci> z </ci> </apply> <apply> <ci> KelvinKer </ci> <ci> &#957; </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> c </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <ci> s </ci> <ci> z </ci> </apply> <apply> <ci> KelvinKei </ci> <ci> &#957; </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </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