Suppose $$R\left ( r \right )=\frac{u\left ( r \right )}{r}$$
Where $$u\left ( r \right )=A\sin\left ( kr \right )+B\cos\left ( kr \right )$$
The boundary condition is $$u\left ( a \right )=0 \wedge |u\left ( 0 \right )|< \infty$$
Indeed, putting the equation in order, we have
$$R\left ( r \right )=\frac{u\left ( r \right )}{r}=\frac{A\sin\left ( kr \right )}{r}+\frac{B\cos\left ( kr \right )}{r}$$
For the boundary condition to hold, we require that B=0 to prevent a blow up of the reciprocal 1 on 0-fair enough
But happens to $$\frac{A\sin\left ( kr \right )}{r}$$ as r tends to zero?
Clearly, the result is indeterminate. How does one get around explaining away the fact that it is alright that is not an issue-physical or mathematical.