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Did an exercise and a small simulation to expand [tex]f(x)=x[/tex], defined on [tex]0<x<3[/tex] in a Fourier-Bessel series using Bessel functions of order one that satisfy the boundary condition [tex]J_1(3\lambda)=0[/tex] and I have some questions:

1.- Is there a rule to use an specific Bessel function order to do the expansion? In other words is it possible to do the expansion using Bessel functions of order 1,2,3...,n? If yes, which criteria does one uses to select the order?

2.- For this particular case, how does the boundary condition can be interpreted? Why does the boundary condition is of order 1?

The reason of my questions is that I would like to expand [tex]f(x)=x^2[/tex] and don't know if it is correct to use Bessel functions of other order than one; for this particular exercise what is the nature of expanding and setting the boundary condition with an specific order.

Thank you

Kind Regards

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# Fourier-Bessel Series Expansion

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