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variants of this functions
KelvinBei






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/03.13.13.0009.01









  


  










Input Form





Derivative[4][w][z] - 4 (Log[r] + Log[s]) Derivative[3][w][z] + 2 (2 Log[r]^2 + 6 Log[r] Log[s] + 3 Log[s]^2) Derivative[2][w][z] + 4 (Log[r] + Log[s]) (-2 Log[r] Log[s] - Log[s]^2) Derivative[1][w][z] + (a^4 r^(4 z) Log[r]^4 + 4 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[a r^z] + Subscript[c, 2] s^z KelvinBei[a r^z] + Subscript[c, 3] s^z KelvinKer[a r^z] + Subscript[c, 4] s^z KelvinKei[a r^z]










Standard Form





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MathML Form







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type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ln /> <ci> r </ci> </apply> <apply> <ln /> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <ln /> <ci> r </ci> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <ci> r </ci> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <ln /> <ci> s </ci> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <ln /> <ci> r </ci> </apply> <apply> <power /> <apply> <ln /> <ci> s </ci> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <apply> <ln /> <ci> r </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ln /> <ci> s </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <eq /> <apply> <ci> w </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> c </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <ci> s </ci> <ci> z </ci> </apply> <apply> <ci> KelvinBer </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> <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> 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Rule Form





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





2007-05-02





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