**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.

**KEYWORD: ** LEGENDRE FUNCTIONS