# Accession Number:

## AD0687108

# Title:

## TABLES OF TOROIDAL HARMONICS, I: ORDERS 0-5, ALL SIGNIFICANT DEGREES.

# Descriptive Note:

## Final scientific rept.,

# Corporate Author:

## AEROSPACE RESEARCH LABS WRIGHT-PATTERSON AFB OHIO

# Personal Author(s):

# Report Date:

## 1969-02-01

# Pagination or Media Count:

## 226.0

# Abstract:

The report contains two eleven-figure tables of the Legendre function of the second kind Qsuperscript usub v-12s 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 - 12 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 1.1.15. 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

# Descriptors:

# Subject Categories:

- Theoretical Mathematics