Here we present improved values for several tables from Sekera and Kahle (1966). The results are split into the X and Y function results (in subdirectory XY) and the K and L function results (in subdirectory KL). The results are tabulated for the following sets of parameters: TAU = 0.15, 0.25, 0.1, 0.50, 0.70, 1.0, 2.0, 4.0, 8.0, 16.0, 100.0 MU = 0.00, 0.02, 0.04, ..., 0.96, 0.98, 1.00 Here, TAU is the optical thickness; MU is the absolute value of the cosine of the zenith distance (Sekera and Kahle, 1966; SK hereon). Tables 1 and 2 of SK are in subdirectory XY. The files for Table 1 are named as follows: XY_TAU_{0.15/0.25/0.1/0.50/0.70/1.0/2.0/4.0/8.0/16.0/100.0} where the filename has one of the argument values. Note that we do not tabulate results for X3, X4, Y3 or Y4 because these functions have nonunique solutions. Table 2 is named XY_MOM. Tables C and D are also in this subdirectory. Tables 3 and 4 of SK are in subdirectory KL. The files for Table 3 are named as follows: KL_TAU_{0.15/0.25/0.1/0.50/0.70/1.0/2.0/4.0/8.0/16.0/100.0} where the filename has one of the argument values. Table 4 is named KL_MOM. Tables A and B are also in this subdirectory. References: 1. Sekera, Z., & Kahle, A. B. 1966, Scattering Functions for Rayleigh Atmospheres of Arbitrary Thickness, Rep. R-452-PR (Santa Monica: The Rand Corporation)