Numerical evaluation of spherical Bessel functions of the first kind (Q1326677)

The paper discusses five algorithms (series expansion, forward recursion, backward recursion, analytical solution, phase and amplitude representation) for computing the spherical Bessel functions \(j(x)\) for real values of \(x\). The first four algorithms are selected for developing a universal and reliable algorithm. Reviewer's remark: The author says: It turns out that the usual algorithms providing the values of the spherical Bessel functions of the fiirst kind, \(j_ l (x)\), have a rather limited range of stability. The author does not show where the cited references fail in this respect. Also, the author seems to be unaware of the set of algorithms developed by \textit{D. E. Amos} [ACM Trans. Math. Software 12, 265-273 (1986; Zbl 0613.65013)] because this important reference would have given the author a different opinion about the availability of reliable software for the Bessel functions.