Upgrading from:

FourierSeries`

FourierSeries, FourierTrigSeries, and FourierCoefficient are part of the Mathematica kernel.
FourierSinCoefficient and FourierCosCoefficient are now in the built-in Mathematica kernel.
DTFourierTransform has been renamed to FourierSequenceTransform.
InverseDTFourierTransform has been renamed to InverseFourierSequenceTransform.
The numerical functions, such as NFourierTransform, are still available in the Fourier Series Package.
The default value of the FourierParameters option has changed for all symbols previously available in the Fourier Series Package.

New system functions

FourierSeries and FourierTrigSeries are now in the built-in Mathematica kernel:

Version 6.0 << FourierSeries` FourierSeries[Sin[t]^2, t, 3]

FourierCoefficient, FourierSinCoefficient, and FourierCosCoefficient are part of the built-in kernel:

Version 6.0 << FourierSeries` FourierCoefficient[t^2 + t, t, n]

DTFourierTransform has been renamed to FourierSequenceTransform and added to the built-in kernel:

Version 6.0 << FourierSeries` DTFourierTransform[1/(2 n + 1)^3, n, ω]

InverseDTFourierTransform has been renamed to InverseFourierSequenceTransform:

Version 6.0 << FourierSeries` InverseDTFourierTransform[Exp[-ω^2], ω, n]

FourierParameters option

The default value of the FourierParameters option has changed for each function as described below.

FourierCoefficient and NFourierCoefficient:

Version 6.0 << FourierSeries` a = 2; b = 5; FourierCoefficient[t + t^2, t, 3, FourierParameters  {a, b}]
Version 6.0 << FourierSeries` a = 2; b = 5; NFourierCoefficient[t + t^2, t, 3, FourierParameters  {a, b}]

FourierSeries and NFourierSeries:

Version 6.0 << FourierSeries` a = 2; b = 5; FourierSeries[t + t^2, t, 3, FourierParameters  {a, b}]
Version 6.0 << FourierSeries` a = 2; b = 5; NFourierSeries[t + t^2, t, 3, FourierParameters  {a, b}]

DTFourierTransform and NDTFourierTransform:

Version 6.0 << FourierSeries` a = 2; b = 5; DTFourierTransform[1/(2 n + 1)^2, n, w, FourierParameters  {a, b}]
Version 6.0 << FourierSeries` a = 2; b = 3; Table[NDTFourierTransform[1/(2 n + 1)^2, n, w, FourierParameters  {a, b}], {w, -1/2, 1/2, 0.3}]

InverseDTFourierTransform and NInverseDTFourierTransform:

Version 6.0 << FourierSeries` a = 2; b = 3; InverseDTFourierTransform[E^(-w^2), w, 3, FourierParameters  {a, b}]
Version 6.0 << FourierSeries` a = 2; b = 3; NInverseDTFourierTransform[E^(-w^2), w, 3, FourierParameters  {a, b}]

FourierSinCoefficient and NFourierSinCoefficient:

Version 6.0 << FourierSeries` a = 3; b = 2; f[t_] := t + t^2; FourierSinCoefficient[f[t], t, 5, FourierParameters  {a, b}]
Version 6.0 << FourierSeries` a = 3; b = 2; f[t_] := t + t^2; Table[NFourierSinCoefficient[f[t], t, n, FourierParameters  {a, b}], {n, 1, 4}]

FourierCosCoefficient and NFourierCosCoefficient:

Version 6.0 << FourierSeries` a = 3; b = 2; f[t_] := t + t^2; FourierCosCoefficient[f[t], t, 6, FourierParameters  {a, b}]
Version 6.0 << FourierSeries` a = 3; b = 2; f[t_] := t + t^2; Table[NFourierCosCoefficient[f[t], t, n, FourierParameters  {a, b}], {n, 1, 5}]

FourierTrigSeries and NFourierTrigSeries:

Version 6.0 << FourierSeries` a = 2; b = 3; FourierTrigSeries[t + t^2, t, 3, FourierParameters  {a, b}]
Version 6.0 << FourierSeries` a = 2; b = 3; NFourierTrigSeries[t + t^2, t, 3, FourierParameters  {a, b}]