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;