D'Alembertian series solutions at ordinary points of LODE with polynomial coefficients

• Autores: S. A. Abramov, Mohammed A. Barkatou
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 44, Nº 1, 2009, págs. 48-59
• Idioma: inglés
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• Resumen

  • By definition, the coefficient sequence of a d�Alembertian series � Taylor�s or Laurent�s � satisfies a linear recurrence equation with coefficients in and the corresponding recurrence operator can be factored into first-order factors over (if this operator is of order 1, then the series is hypergeometric). Let L be a linear differential operator with polynomial coefficients. We prove that if the expansion of an analytic solution u(z) of the equation L(y)=0 at an ordinary (i.e., non-singular) point of L is a d�Alembertian series, then the expansion of u(z) is of the same type at any ordinary point. All such solutions are of a simple form. However the situation can be different at singular points