Sampling series for band-limited generalized functions

For an arbitrary band-limited generalized function a representation is obtained that is a combination of a Taylor series and a conventional sampling series. A parameter that enters can be chosen such as to make the series rapidly convergent. Furthermore, it is shown that, for suitably restricted test functions, can be represented by a conventional sampling series and by a series of delta functions with weights equal to the sampling values. The results apply also to ordinary band-limited functions.