*DECK DQMOMO SUBROUTINE DQMOMO (ALFA, BETA, RI, RJ, RG, RH, INTEGR) C***BEGIN PROLOGUE DQMOMO C***PURPOSE This routine computes modified Chebyshev moments. The K-th C modified Chebyshev moment is defined as the integral over C (-1,1) of W(X)*T(K,X), where T(K,X) is the Chebyshev C polynomial of degree K. C***LIBRARY SLATEC (QUADPACK) C***CATEGORY H2A2A1, C3A2 C***TYPE DOUBLE PRECISION (QMOMO-S, DQMOMO-D) C***KEYWORDS MODIFIED CHEBYSHEV MOMENTS, QUADPACK, QUADRATURE C***AUTHOR Piessens, Robert C Applied Mathematics and Programming Division C K. U. Leuven C de Doncker, Elise C Applied Mathematics and Programming Division C K. U. Leuven C***DESCRIPTION C C MODIFIED CHEBYSHEV MOMENTS C STANDARD FORTRAN SUBROUTINE C DOUBLE PRECISION VERSION C C PARAMETERS C ALFA - Double precision C Parameter in the weight function W(X), ALFA.GT.(-1) C C BETA - Double precision C Parameter in the weight function W(X), BETA.GT.(-1) C C RI - Double precision C Vector of dimension 25 C RI(K) is the integral over (-1,1) of C (1+X)**ALFA*T(K-1,X), K = 1, ..., 25. C C RJ - Double precision C Vector of dimension 25 C RJ(K) is the integral over (-1,1) of C (1-X)**BETA*T(K-1,X), K = 1, ..., 25. C C RG - Double precision C Vector of dimension 25 C RG(K) is the integral over (-1,1) of C (1+X)**ALFA*LOG((1+X)/2)*T(K-1,X), K = 1, ..., 25. C C RH - Double precision C Vector of dimension 25 C RH(K) is the integral over (-1,1) of C (1-X)**BETA*LOG((1-X)/2)*T(K-1,X), K = 1, ..., 25. C C INTEGR - Integer C Input parameter indicating the modified C Moments to be computed C INTEGR = 1 compute RI, RJ C = 2 compute RI, RJ, RG C = 3 compute RI, RJ, RH C = 4 compute RI, RJ, RG, RH C C***REFERENCES (NONE) C***ROUTINES CALLED (NONE) C***REVISION HISTORY (YYMMDD) C 820101 DATE WRITTEN C 891009 Removed unreferenced statement label. (WRB) C 891009 REVISION DATE from Version 3.2 C 891214 Prologue converted to Version 4.0 format. (BAB) C***END PROLOGUE DQMOMO C DOUBLE PRECISION ALFA,ALFP1,ALFP2,AN,ANM1,BETA,BETP1,BETP2,RALF, 1 RBET,RG,RH,RI,RJ INTEGER I,IM1,INTEGR C DIMENSION RG(25),RH(25),RI(25),RJ(25) C C C***FIRST EXECUTABLE STATEMENT DQMOMO ALFP1 = ALFA+0.1D+01 BETP1 = BETA+0.1D+01 ALFP2 = ALFA+0.2D+01 BETP2 = BETA+0.2D+01 RALF = 0.2D+01**ALFP1 RBET = 0.2D+01**BETP1 C C COMPUTE RI, RJ USING A FORWARD RECURRENCE RELATION. C RI(1) = RALF/ALFP1 RJ(1) = RBET/BETP1 RI(2) = RI(1)*ALFA/ALFP2 RJ(2) = RJ(1)*BETA/BETP2 AN = 0.2D+01 ANM1 = 0.1D+01 DO 20 I=3,25 RI(I) = -(RALF+AN*(AN-ALFP2)*RI(I-1))/(ANM1*(AN+ALFP1)) RJ(I) = -(RBET+AN*(AN-BETP2)*RJ(I-1))/(ANM1*(AN+BETP1)) ANM1 = AN AN = AN+0.1D+01 20 CONTINUE IF(INTEGR.EQ.1) GO TO 70 IF(INTEGR.EQ.3) GO TO 40 C C COMPUTE RG USING A FORWARD RECURRENCE RELATION. C RG(1) = -RI(1)/ALFP1 RG(2) = -(RALF+RALF)/(ALFP2*ALFP2)-RG(1) AN = 0.2D+01 ANM1 = 0.1D+01 IM1 = 2 DO 30 I=3,25 RG(I) = -(AN*(AN-ALFP2)*RG(IM1)-AN*RI(IM1)+ANM1*RI(I))/ 1 (ANM1*(AN+ALFP1)) ANM1 = AN AN = AN+0.1D+01 IM1 = I 30 CONTINUE IF(INTEGR.EQ.2) GO TO 70 C C COMPUTE RH USING A FORWARD RECURRENCE RELATION. C 40 RH(1) = -RJ(1)/BETP1 RH(2) = -(RBET+RBET)/(BETP2*BETP2)-RH(1) AN = 0.2D+01 ANM1 = 0.1D+01 IM1 = 2 DO 50 I=3,25 RH(I) = -(AN*(AN-BETP2)*RH(IM1)-AN*RJ(IM1)+ 1 ANM1*RJ(I))/(ANM1*(AN+BETP1)) ANM1 = AN AN = AN+0.1D+01 IM1 = I 50 CONTINUE DO 60 I=2,25,2 RH(I) = -RH(I) 60 CONTINUE 70 DO 80 I=2,25,2 RJ(I) = -RJ(I) 80 CONTINUE RETURN END