Riccati-Bessel Functions

$$S_n(z) \equiv zj_n(z) = \sqrt{\pi z\over 2} J_{n+1/2}(z)$$

$$C_n(z) \equiv -zn_n(z) = -\sqrt{\pi z\over 2} N_{n+1/2}(z),$$

where $j_n(z)$ and $n_n(z)$ are Spherical Bessel Functions of the First and Second Kind.

References

Abramowitz, M. and Stegun, C. A. (Eds.). ``Riccati-Bessel Functions.'' §10.3 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 445, 1972.