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Rayleigh's Formulas

The formulas

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

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.




© 1996-9 Eric W. Weisstein
1999-05-25