Rayleigh's Formulas

The formulas

$$j_n(z) = z^n\left({-{1\over z}{d\over dz}}\right)^n{\sin z\over z}$$

$$y_n(z) = -z^n\left({-{1\over z}{d\over dz}}\right)^n{\cos z\over z}$$

for $n=0$, 1, 2, ..., where $j_n(z)$ is a Spherical Bessel Function of the First Kind and $y_n(z)$ is a Spherical Bessel Function of the Second Kind.

References

Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 439, 1972.