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Riccati-Bessel Functions

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

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


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.

© 1996-9 Eric W. Weisstein