File: fourie.usg

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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