C330: Legendre and Associated Legendre Functions

Author(s): K.S. Kölbig Library: MATHLIB
Submitter: Submitted: 15.05.1987
Language: Fortran Revised: 01.12.1994

Subroutine subprograms RASLGF and DASLGF calculate, for a given real argument tex2html_wrap_inline133 , and a given integer value of the order m, a sequence of either unnormalized or normalized Legendre (m=0) or Associated Legendre tex2html_wrap_inline139 functions of degree tex2html_wrap_inline141 , defined by

displaymath143

respectively, where

displaymath145

is the Legendre polynominal of degree n. Note that some authors use an additional factor tex2html_wrap_inline149 in the definition (1).

On CDC and Cray computers, the double-precision version DASLGF is not available.

Structure:

SUBROUTINE subprograms
User Entry Names: RASLGF, DASLGF
Obsolete User Entry Names: ASLGF tex2html_wrap_inline151 RASLGF
Files Referenced: Unit 6
External References: MTLMTR, ABEND

Usage:

For tex2html_wrap_inline153 (type REAL), tex2html_wrap_inline155 (type DOUBLE PRECISION),

    CALL tASLGF(MODE,X,M,NL,P)
MODE
(INTEGER) tex2html_wrap_inline157 Unnormalized functions (1),
(INTEGER) tex2html_wrap_inline159 Normalized functions (2).
X
(type according to t) The argument x.
M
(INTEGER) The order m (upper index) of all functions in the computed sequence. It is permissible for M to be negative.
NL
(INTEGER) Specifies the degree N of the last function in the computed sequences.
P
(type according to t) One-dimensional array of dimension (0:d) where tex2html_wrap_inline167 .
On exit, tex2html_wrap_inline169 , contains tex2html_wrap_inline171 or tex2html_wrap_inline173 as specified by MODE. (See Notes).

Method:

The functions tex2html_wrap_inline175 are for m>0 calculated by means of the standard recurrence relation.

Restrictions:

  1. tex2html_wrap_inline179 .
  2. tex2html_wrap_inline181 or 2.
  3. If tex2html_wrap_inline183 :
    if tex2html_wrap_inline185 and tex2html_wrap_inline187 ; ( tex2html_wrap_inline189 on VAX/VMS).

Accuracy:

RASLGF (except on CDC and Cray computers) has full single-precision accuracy. For most values of the argument X, DASLGF (and RASLGF on CDC and Cray computers) has an accuracy of approximately two significant digits less than the machine precision.

Notes:

In accordance with the definitions, tex2html_wrap_inline191 for tex2html_wrap_inline193 .

Error handling:

Error C330.1: tex2html_wrap_inline195 .
Error C330.2: tex2html_wrap_inline197 and tex2html_wrap_inline199 .
Error C330.3: tex2html_wrap_inline201 and tex2html_wrap_inline203 incompatible.
In all cases, a message is written on Unit 6, unless subroutine MTLSET (N002) has been called. The initial contents of array P(n) is left unchanged.
tex2html_wrap_inline205


Michel Goossens Tue Jun 4 22:04:38 METDST 1996