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 , and a given integer value of the order m, a sequence of either unnormalized or normalized Legendre (m=0) or Associated Legendre functions of degree , defined by
respectively, where
is the Legendre polynominal of degree n. Note that some authors use an additional factor 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 RASLGF
Files Referenced: Unit 6
External References: MTLMTR, ABEND
Usage:
For (type REAL), (type DOUBLE PRECISION),
CALL tASLGF(MODE,X,M,NL,P)
Method:
The functions are for m>0 calculated by means of the standard recurrence relation.
Restrictions:
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, for .
Error handling:
Error C330.1: .
Error C330.2: and .
Error C330.3: and 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.