NUMAL Section 2.4.3
BEGIN SECTION : 2.4.3 (October, 1974)
AUTHOR : C.G. VAN DER LAAN.
INSTITUTE : RIJKSUNIVERSITEIT GRONINGEN.
RECEIVED : 740131.
BRIEF DESCRIPTION :
INTCHS COMPUTES THE INDEFINITE INTEGRAL OF A GIVEN CHEBYSHEV
SERIES.
KEYWORDS :
INDEFINITE INTEGRATION,
CHEBYSHEV SERIES.
CALLING SEQUENCE :
THE HEADING OF THE PROCEDURE READS :
"PROCEDURE"INTCHS(N,A,B);
"VALUE"N;"INTEGER"N;"ARRAY"A,B;
"CODE" 31248;
THE MEANING OF THE FORMAL PARAMETERS IS :
N : <ARITHMETIC EXPRESSION>;
ENTRY:
THE DEGREE OF THE POLYNOMIAL REPRESENTED BY THE CHEBYSHEV
SERIES;
A,B: <ARRAY IDENTIFIER>;
"ARRAY" A[0:N],B[1:N+1];
ENTRY:
THE COEFFICIENTS OF THE CHEBYSHEV SERIES,A[0]+A[1]*T1(X)+...+
+A[N]*TN(X),SHOULD BE GIVEN IN ARRAY A.
EXIT:
THE COEFFICIENTS OF THE INTEGRAL CHEBYSHEV SERIES,
B[1]*T1(X)+...+B[N+1]*TN+1(X), ARE DELIVERED IN ARRAY B.
(T1(X),...TN+1(X) DENOTE CHEBYSHEV POLYNOMIALS OF THE FIRST
KIND,OF DEGREE 1,...N+1,RESPECTIVELY).
METHOD AND PERFORMANCE :
FOR A DESCRIPTION OF THE ALGORITHM SEE AMONG OTHERS :
CLENSHAW,1962,P.11,OR FOX AND PARKER,1968,P.59.
REFERENCES :
BROUCKE,R.(1973):
TEN SUBROUTINES FOR THE MANIPULATION OF CHEBYSHEV SERIES.
ALGORITHM 446.(FORTRAN).
COMM.ACM,VOL.16,1,P.254-256.
CLENSHAW,C.W.(1962):
CHEBYSHEV SERIES FOR MATHEMATICAL FUNCTIONS.
MATH.TAB.NAT.PHYS.LAB. 5,LONDON.
H.M. STATIONARY OFFICE.
FOX,L.&I.B.PARKER(1968):
CHEBYSHEV POLYNOMIALS IN NUMERICAL ANALYSIS.
OXFORD UNIVERSITY PRESS.
EXAMPLE OF USE :
AS A FORMAL TEST OF THE PROCEDURE INTCHS THE CHEBYSHEV SERIES :
1+1/2*T1(X)+1/5*T2(X)+1/10*T3(X) IS TRANSFORMED INTO ITS INTEGRAL.
"BEGIN""ARRAY"A[0:3],B[1:4];
A[0]:=1;A[1]:=.5;A[2]:=.2;A[3]:="-1;
INTCHS(3,A,B);
OUTPUT(61,"("/,4(BZ.4D)")",B[1],B[2],B[3],B[4]);
"END"
.9000 .1000 .0333 .0125
SOURCE TEXT(S):
"CODE" 31248;