## Expansion of a Bessel Function

1. The problem statement, all variables and given/known data
Since the expansion of:
$$J_0(x)=1-\frac{x^2}{2^2}+\frac{1}{(2!)^2}\frac{x^4}{2^4}....$$
Is the expansion of:
$$J_0(ax)$$
$$J_0(ax)=1-\frac{(ax)^2}{2^2}+\frac{1}{(2!)^2}\frac{(ax)^4}{2^4}....$$

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution