Mathematical Tables

Mathematical Tables of In ? (z) for Complex Argument is a compilation of tables of In ? (z), z = x + iy, calculated for steps in x and y of 0.01 and with an accuracy of one unit in the last (the sixth) decimal place. Interpolation is used to calculate In ? (z) for intermediate values and is carried out separately for the real and imaginary parts of In ? (z). Six places are retained in interpolation. This book first explains how the values of In ? (z) are calculated using the asymptotic formula in a wide lattice with step h = 0.16, and how the tables and the nomograph are used. The values in the lattice are interpolated successively at the centers of various symmetric figures. The calculation of In ? (z) outside the quadrangle is also considered. Formulas for the calculation of In ? (z) outside the given rectangle are listed. The nomograph is intended to facilitate the interpolation procedure. Some of the calculations (including the rounding off of the results to the sixth place and the calculation of second differences) are carried out with the aid of analytical computers. This monograph will be of interest to mathematicians and mathematics students.