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```SUBROUTINE FORIT

PURPOSE
FOURIER ANALYSIS OF A PERIODICALLY TABULATED FUNCTION.
COMPUTES THE COEFFICIENTS OF THE DESIRED NUMBER OF TERMS
IN THE FOURIER SERIES F(X)=A(0)+SUM(A(K)COS KX+B(K)SIN KX)
WHERE K=1,2,...,M TO APPROXIMATE A GIVEN SET OF
PERIODICALLY TABULATED VALUES OF A FUNCTION.

USAGE
CALL FORIT(FNT,N,M,A,B,IER)

DESCRIPTION OF PARAMETERS
FNT-VECTOR OF TABULATED FUNCTION VALUES OF LENGTH 2N+1
N  -DEFINES THE INTERVAL SUCH THAT 2N+1 POINTS ARE TAKEN
OVER THE INTERVAL (0,2PI). THE SPACING IS THUS 2PI/2N+1
M  -MAXIMUM ORDER OF HARMONICS TO BE FITTED
A  -RESULTANT VECTOR OF FOURIER COSINE COEFFICIENTS OF
LENGTH M+1
A SUB 0, A SUB 1,..., A SUB M
B  -RESULTANT VECTOR OF FOURIER SINE COEFFICIENTS OF
LENGTH M+1
B SUB 0, B SUB 1,..., B SUB M
IER-RESULTANT ERROR CODE WHERE
IER=0  NO ERROR
IER=1  N NOT GREATER OR EQUAL TO M
IER=2  M LESS THAN 0

REMARKS
M MUST BE GREATER THAN OR EQUAL TO ZERO
N MUST BE GREATER THAN OR EQUAL TO M
THE FIRST ELEMENT OF VECTOR B IS ZERO IN ALL CASES

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
NONE

METHOD
USES RECURSIVE TECHNIQUE DESCRIBED IN A. RALSTON, H. WILF,
'MATHEMATICAL METHODS FOR DIGITAL COMPUTERS', JOHN WILEY
AND SONS, NEW YORK, 1960, CHAPTER 24. THE METHOD OF INDEXING
THROUGH THE PROCEDURE HAS BEEN MODIFIED TO SIMPLIFY THE
COMPUTATION.

```