On the validity of localized approximations for Bessel beams: All N-Bessel beams are identically equal to zero

•Localized approximation has been used to evaluate BSCs of Bessel beams.•N-beam procedure fails to provide a localized approximation for Bessel beams.•Localized approximation should be used only for small axicon angles.

Localized approximation procedures are efficient ways to evaluate beam shape coefficients of a laser beam. They are particularly useful when other methods are ineffective or inefficient. Several papers in the literature have reported the use of such procedures to evaluate the beam shape coefficients of Bessel beams. Relying on the concept of N-beams, it is demonstrated that care must be taken when constructing a localized approximation for a Bessel beam, namely a localized Bessel beam is satisfactorily close enough to the intended beam only when the axicon angle is small enough.