Polynomial solutions of certain differential equations arising in physics
نویسندگان
چکیده
Conditions for the existence of polynomial solutions of certain second-order differential equations have recently been investigated by several authors. In this paper a new algorithmic procedure is given to determine necessary and sufficient conditions for a differential equation with polynomial coefficients containing parameters to admit polynomial solutions and to compute these solutions. The effectiveness of this approach is illustrated by applying it to determine new solutions of several differential equations of current interest. A comparative analysis is given to demonstrate the advantage of this algorithmic procedure over existing software.
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