Tables of Toroidal Harmonics, I: Orders 0-5, All Significant Degrees

摘要

The report contains two eleven-figure tables of the Legendre function of the second kind Q(superscript u)(sub v-1/2)(s) for integral values of u and v and s > 1. These functions, also known as toroidal harmonics, occur in the solution of potential problems involving a torus-shaped boundary, as well as in other practical areas. The parameter u, usually referred to as the 'order' is taken up to r and v (v - 1/2 is known as the 'degree') is allowed to vary from 0 to a value for which the absolute value of the function is less than 10 to the minus 12 power, for the largest value of u considered. The argument in first set of tables is taken as s and covers the range s = 1.1(.1)5. In the second set the argument is taken as cosh (n) which is a more natural parameter to use in the solution of the potential problem in toroidal coordinates. (Author)