ELISE, an algorithm to compute asymptotic representations for solutions of linear differential equations, realized with the computer algebra system MAPLE. ELISE is a package of procedures implemented in MAPLE to compute asymptotic representations for solutions of linear irregular singular differential equations with rational coefficients. The algorithm allows the use of parameters, so that classes of differential equations can be treated in their entirety. Some ideas have been realized in ELISE to make it efficient and easy usable. In each step it is checked, which coefficients in the differential equation have influence and which do not. It may be noted that ELISE was developed in 1988 independently of other programs, e.g. DESIR.

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