A modification of the kummer's method for efficient computation of the 2-D Green's functions for 1-D periodic structures

A new modification of the Kummer's method of Mth order for 2≤M≤6 is proposed for efficient computation of the 2-D Green's function for 1-D periodic structures in homogeneous media. The modification consists in transformation of the auxiliary series constructed of asymptotic terms of the original spectral series into a new series which, unlike the previous one, allows its summation in closed form. The new representation of the Green's functions consists of a rapidly converging difference series whose terms decay as q−(M+1), as well a new rigorous expression for the sum of the transformed auxiliary series.