Polynomial approximations to Bessel functions
Bessel functions appear in numerous physical problems, and play an important role in many electromagnetic scattering problems. There is no closed form expression for Bessel functions so that approximations suitable for numerical evaluation are necessary in applications. Gross  has derived interesting polynomial approximations to the zerothand first-order Bessel functions of the first kind for small arguments, that arise from an integral that occurs in an electromagnetic scattering problem. We study here in detail properties of these approximations. First we extend the analysis in  to derive corresponding polynomial approximations for Bessel functions of any integer order. Second we show that as the degree of the polynomial approximation increases, it converges to the Taylor series expansion. Third we compare the accuracy of the polynomial approximations to that of the truncated Taylor series of the same order.