How to express a function f(x) as a Fourier-Bessel series

It turns out that we can represent a function f(x) as a linear combination of Bessel functions (solutions to the parametric Bessel equation). There are three special cases given the frontier conditions. In this example, we take two of these cases to represent f(x) = x as a Fourier-Bessel series. We have a lesson where we showed where the definitions of this lesson come from    • The complete definition of the Fourier-Bes...   And, we have other two lessons where we look deep into the origin of the Fourier Bessel series, the parametric Bessel equation and the Sturm-Liouville problem, necessary to understand this topic.    • How to construct the Fourier-Bessel series?      • The self-adjoint form for a second order d...   And, you can follow this content on instagram!   / mathephyks