Math code
Fun and games with Mathematica
Bessel functions in the transition region
This Mathematica notebook computes asymptotic expansions of Bessel functions when both the argument and order are large, where the usual asymptotic series are inaccurate. It uses F. W. J. Olver’s 1952 technique, can compute the expansion to arbitrary orders, and includes 28 computed terms.
Download the Mathematica notebook (.nb) · NIST DLMF reference
Zeros of Bessel functions
The notebook also computes asymptotic expansions of the zeros of Bessel functions and their derivatives, using Olver’s 1951 technique. It can compute these expansions to arbitrary orders, and contains another 19 computed terms beyond the original expansions.
Download the Mathematica notebook (.nb) · NIST DLMF reference