Factoring and splitting of s-differential equations in the field of mikusinski

Abstract

Applying the Laplace tracsformation we obtain simple formulas for Bessel fuctions (see Ince [2])Also,Mikusinski's operational calculus provides simple formulas for the solutions of the Laguerre equation,the hypergeometric equation and of other differential equations (see Kierat,Skornik [4]and Yosida [13]).the question arises:does operational calculus always lead to a simplification,or is it just an accident for some equations? Using differential algebra (see Kolchin [6],Ritt[9]and other), we will get some amswers to this question.

Keywords:

• operational calculus
• linear differential equations
• differential algebra

MSC(1991):

• 34A25
• 44A40