  We make a critical, next-to-leading order, study of the relationship between
the longitudinal structure function FL and the gluon distribution proposed in
Cooper- Sarkar et al. (Z. Phys. C 39:281, 1988; Acta Phys. Pol. B 34:2911
2003), which is frequently used to extract the gluon distribution from the
proton longitudinal structure function at small x. The gluon density is
obtained by expanding at particular choices of the point of expansion and
compared with the hard Pomeron behavior for the gluon density. Comparisons with
H1 data are made and predictions for the proposed best approach are also
provided.
