(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I want to make sure that a solution to a differrential equation given by bessel functions of the first kind and second kind meet at a border(r=a), and it to be differenitable. So i shall determine the constants c_1 and c_2

I use notation from Schaums outlines

2. Relevant equations

The functions:

[itex]R_1 = c_1J_\gamma(\kappa r),\hspace{8pt}r\in [0,a]\\

R_2 = c_2K_\gamma(\sigma r),\hspace{8pt}r\in[a,b][/itex]

3. The attempt at a solution

For the solution to be continous at r=a:

[itex] c_1J_\gamma(\kappa a) = c_2K_\gamma(\sigma a)[/itex]

For it to be differentiable:

[itex] c_1J'_\gamma(\kappa a) = c_2K'_\gamma(\sigma a)[/itex]

I tried taking the determinant of the matrix describing the system at set it equal to zero, but i didn't seem to work. I also know from another part of the problem, that [itex]\gamma\in\mathbb{Z}[/itex]

But is there a trick i've missed?

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# Homework Help: Bessel functions continuity

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