Spherical expansions of sound radiation from a finite line source with reduced error

The sound pressure due to a finite length line source is calculated using a spherical harmonic expansion. An improved expansion is then derived which uses a small argument approximation for the product of a spherical Bessel and Hankel function and exploits the fact that the approximation also works when the order is large compared to the argument. The higher order terms can then be approximated using the equivalent potential integral. This method can be applied to any calculation of radiated fields using spherical expansions. The improved expansion is most useful for the calculation of the sound pressure in the near field.