1. NAME AND TITLE

LEGENDRE FUNCTIONS: Legendre Functions of the First Kind and Legendre Polynomials.

AUXILIARY ROUTINES

TLP: Provides Tables of Legendre Polynomials.

TALP: Provides Tables of Associated Legendre Polynomials.

TDER

HARM

DER

2. CONTRIBUTOR

Lawrence Livermore National Laboratory, Livermore, California.

3. CODING LANGUAGE AND COMPUTER

Fortran IV; IBM 360/370.

4. NATURE OF PROBLEM SOLVED

Routines in the package calculate the associated Legendre functions of the first kind, indefinite (multiple) integrals involving the Legendre polynomials, derivatives of the Legendre polynomials, spherical harmonic functions, and an expansion of an arbitrary (single valued) function.

5. METHOD OF SOLUTION

LEGENDRE FUNCTIONS contains routines to expand functions in Legendre polynomials, routines for the real and imaginary parts of the spherical harmonics in spherical polar coordinates, derivatives of the Legendre polynomials and multiple integrals of Legendre polynomials P_k(X) multiplied by a positive integer power of X. Derivations of the mathematical formulae used are included in the documentation.

6. RESTRICTIONS OR LIMITATIONS

None noted.

7. TYPICAL RUNNING TIME

No study has been made by RSIC of typical running times for LEGENDRE FUNCTIONS.

8. COMPUTER HARDWARE REQUIREMENTS

LEGENDRE FUNCTIONS is operable on the IBM 360/370 computers.

9. COMPUTER SOFTWARE REQUIREMENTS

A Fortran IV compiler is required.

10. REFERENCE

G. R. Gathers, "Routines Using Associated Legendre Functions and Legendre Polynomials," UCRL-52127 (January 1977).

11. CONTENTS OF CODE PACKAGE

Included are the referenced document and one (1.2MB) DOS diskette which contains the source code and sample problem input and output.

12. DATE OF ABSTRACT

March 1984; reviewed May 1984.