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

nuclear physics a

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