Info on Bessel functions & their use as basis functions.

[lievbirman]

Hello all,As an exercise my research mentor assigned me to solve the following set of equations for the constants a, b, and c at the bottom. The function f(r) should be a basis function for a cylindrical geometry with boundary conditions such that the value of J is 0 at the ends of the cylinder.

I'm having trouble finding textbooks with the information I must know to solve these equations. If anyone can point me in the right direction I would be very grateful. From what I understand thus far, the functions should be some variant of Bessel functions, and this method is that of basis functions.

 

[SteamKing]

These wiki articles give a list of references which you can research:

http://en.wikipedia.org/wiki/Bessel_function

http://en.wikipedia.org/wiki/Cylindrical_harmonics

Then, there is the granddaddy of references for the Bessel functions, namely G N Watson, A Treatise on the Theory of Bessel Functions, which is located on the Internet Archive:

https://archive.org/details/ATreatiseOnTheTheoryOfBesselFunctions