[en] Laguerre, Hermite and Legendre polynomial bases were studied for high order time expansions of reactor kinetics solutions. A theorem showing an exponential majoring function for the solution of bounded reactivity transients introduce Laguerre, Hermite and Legendre polynomials for semi-infinite, infinite and finite time domains, respectively. The numerical solutions were obtained by means of the construction of an error estimator and its minimization using a conventional variational method. Some point reactor kinetics problems with exact solution were tested. The results showed a numerical monotone convergent behavior and accuracy, but problem-dependent efficiency caused by the extremely large expansion orders (more than 200 terms) needed in the studied bases for the cases with large reactivity insertions. (author)