Analytical solution of the longitudinal structure function $F_L$ 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 $x$