Abstract
An infinite-order linear differential equation with constant coefficients and characteristic equation of the class [1, 0] is investigated, and a class of solutions is introduced. It is shown that, if the zeros λk =αk+ iΒk of the characteristic function satisfy the condition\(\mathop {\lim }\limits_{k \to \infty } \left| {\frac{{\lambda _k }}{{\beta _k }}} \right| > 0\), then all solutions of the class under consideration are analytic functions.
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