#!/usr/bin/env python3 import mpmath as mp # APPLIED OPTICS / Vol. 53, No. 31 / 1 November 2014, eq(13) def LeRu_cutoff(z): x = mp.fabs(z) return int(x + 11 * x**(1/3) + 1) # Riccati-Bessel z*j_n(z) def psi(n,z): return mp.sqrt( (mp.pi * z)/2 ) * mp.autoprec(mp.besselj)(n+1/2,z) # to compare r(n,z) with Wolfram Alpha # n=49, z=1.3-2.1i, SphericalBesselJ[n-1,z]/SphericalBesselJ[n,z] def r(n,z): if n > 0: return psi(n-1,z)/psi(n,z) return mp.cos(z)/mp.sin(z) def D1(n,z): return r(n,z) - n/z
