Analysis of the proton longitudinal structure function from the gluon distribution function

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.