Abstract
Define\(D = \frac{d}{{dx}}\) and let L(D)=∑ai(x)Di∈φ[x][D] be a linear differential operator with polynomial coefficients. G. POLYA for L(D)=D and D. CANTOR for L(D)=P(xD), P∈φ[x] proved that if u∈ℤ[[x]] is such that L(D)(u) is a rational function, then u is also a rational function.
In this paper, we introduce a new class of linear differential operators with the same property.
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Bezivin, JP. Une propriete arithmetique de certains operateurs differentiels. Manuscripta Math 57, 351–372 (1987). https://doi.org/10.1007/BF01437487
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DOI: https://doi.org/10.1007/BF01437487