Spherical Bessel function
= Spherical Bessel function
{c}
{title2=$j_\ell(x)=\sqrt{\pi/(2x)}J_{\ell+1/2}(x)$}
The spherical Bessel functions solve the radial wave equation in three dimensions. In particular,
$$
j_2(x)=\left(\frac3{x^3}-\frac1x\right)\sin x-\frac3{x^2}\cos x,
\qquad j_2(x)=\frac{x^2}{15}+O(x^4).
$$
The apparent singularity at the origin is removable, as follows from the power series of the <Bessel function of the first kind>.