## File: fourie.usg

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maxima 5.6-17
 `123456789101112131415161718192021222324252627282930313233343536373839404142434445464748` ``````EQUALP(X, Y) returns TRUE if X EQUALs Y otherwise FALSE (doesn't give an error message like EQUAL(X, Y) would do in this case) REMFUN(FUN, EXP) replaces all occurrences of FUN(ARG) by ARG in EXP REMFUN(FUN, EXP, VAR) replaces all occurrences of FUN(ARG) by ARG in EXP only if ARG contains the variable VAR FUNP(FUN, EXP) true if EXP contains the function FUN FUNP(FUN, EXP, VAR) true if EXP contains the function FUN and the variable VAR is somewhere in the argument of one of the occurences of FUN ABSINT(FUN, VAR, HALFPLANE) indefinite integral of FUN with respect to VAR in the given halfplane (POS, NEG, or BOTH). If HALFPLANE is omitted, POS is assumed as a default. FUN may contain expressions of the form ABS(X), ABS(SIN(X)), ABS(A)*EXP(-ABS(B)*ABS(X)) ABSINT(FUN, VAR, A, B) definite integral of FUN with respect to VAR from A to B. FUN may include absolute values FOURIER(F, X, P) produces a list of the Fourier coefficients of F(X) defined on the interval [-P, P] FOURSIMP(L) simplifies SIN(N %PI) to 0 if SINNPIFLAG [TRUE] is TRUE and COS(N %PI) to (-1)^N if COSNPIFLAG [TRUE] is TRUE FOUREXPAND(L, X, P, LIMIT) generates the Fourier series from the list of Fourier coefficients L up thru LIMIT terms (LIMIT may be INF). X and P have same meaning as in FOURIER FOURCOS(F, X, P) Fourier cosine coefficients for F(X) defined on [0, P] FOURSIN(F, X, P) Fourier sine coefficients for F(X) defined on [0, P] TOTALFOURIER(F, X, P) := FOUREXPAND(FOURSIMP(FOURIER(F, X, P)), X, P, 'INF) FOURINT(F, X) creates a list of the Fourier integral coefficients of F(X) defined on [MINF, INF] FOURINTCOS(F, X) Fourier cosine integral coefficients for F(X) on [0, INF] FOURINTSIN(F, X) Fourier sine integral coefficients for F(X) on [0, INF] ---MIKE@MIT-MC ``````