A type of bell-shaped compact high-order window function &psgr;(x,y) is studied, and closed-form and approximation formulas are derived for its Hankel transforms. Applications of these results are presented as fast algorithms for calculating dyadic Green's functions for electromagnetic scattering in multilayered media. Numerical results in electromagnetics are provided to demonstrate the accuracy and efficiency of the algorithms. ¿ 2001 American Geophysical Union