Riccati-Bessel S

The Riccati-Bessel function $S_n$ is defined by the formula $$S_n(z)=\sqrt{ \dfrac{\pi x}{2} } J_{n+\frac{1}{2}}(z),$$ where $\pi$ denotes pi and $J_{n+\frac{1}{2}}$ denotes the Bessel function of the first kind.