Computations of light scattering require finding Bessel functions of a series of orders. These are found most easily by recurrence, but excessive rounding errors may accumulate. Satisfactory procedures for cylinder and sphere functions are described. If argument z is real, find Yn(z) by recurrence to high orders. From two high orders of Yn(z) estimate Jn(z). Use backward recurrence to maximum Jn(z). Correct by forward recurrence to maximum. If z is complex, estimate high orders of Jn(z) without Yn(z) and use backward recurrence.
William D. Ross, "Computation of Bessel Functions in Light Scattering Studies," Appl. Opt. 11, 1919-1923 (1972)