Bessel Function

Questions
1

Dear All,

I have a problem with Bessel function, I am new to this concept and I am unable to solve an equation or nor do i know how to solve this. It’s the case of diffusion 2nd law in a cylinder and the resulting equation is,
X= 2/a n=1…infinity? (J0(bn,r)) / (bnJ1(bn,a)) exp (-Dbn^2t) Here bn is root of J0(bna)=0 and J0(bnr) is the bessel function of first kind of order zero and J0 and J1 are bessel functions of the first kind and of order zero and one respectively. I have no idea of what is the value of bn or what is j0 and J1 are. Please help me out. Any suggestions are welcome.

Thank you

2

Mathematica uses BesselJ[0,n] and BesselJ[1,n] notation for the Bessel functions.

Mathematica uses Sum[expression,{n,1,Infinity}] notation for an infinite sum over n.

Mathematica uses various different methods, like Solve[expression==0,b], for finding zeros of expressions.

Can you attempt to express your problem using equations and some of this notation?