Analytical solution of the longitudinal structure function FL in the leading and next-to-leading-order analysis at low x with respect to Laguerre polynomials method

The aim of the present paper is to apply the Laguerre polynomials method for the analytical solution of the Altarelli–Martinelli equation. We use this method of the low-x gluon distribution to the longitudinal structure function using MRST partons as input. Having checked that this model gives a good description of the data to predict of the longitudinal structure function at leading and next-to-leading-order analysis at low x.