While the geometric mean is more rarely used than the arithmetic mean (and the latter can be assumed if not stated explicitly) the former is considered more mathematically rigorous. It more properly reflects the logarithmic relationship of fractional bandwidth with increasing frequency. For narrowband applications, there is only marginal difference between the two definitions. The geometric mean version is inconsequentially slightly larger. For wideband applications they diverge substantially with the arithmetic mean version approaching 2 in the limit and the geometric mean version approaching infinity.