Integral estimates for Laguerre polynomials with exponential weight function

In this paper we consider the system of functions $\lambda_{1+n}(x)$ generated by the system of Laguerre function. For the functions $\lambda_{1+n}(x)$ different representations in terms of the Laguerre polynomials $L_n^\alpha(x)$ are obtained. Using these representations and asymptotic formulas for the $L_n^\alpha(x)$ polynomials, we investigated the behavior of the functions $\lambda_{1+n}(x)$ on $[0,\infty)$ as $n\rightarrow\infty$ and obtained estimates similar to those for the Laguerre functions