Solution of a second-order linear differential equation with polynomial coefficients and Fuchsian point at zero

We specify the structure of the power series determining a solution of a Fuchsian second-order differential equation with polynomial coefficients in a neighborhood of zero. The power series is represented via hypergeometric functions of fractional order. The structure of the coefficients of the seri...

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Veröffentlicht in:	Differential equations 2011, Vol.47 (1), p.20-28
1. Verfasser:	Kruglov, V. E.
Format:	Artikel
Sprache:	eng
Schlagworte:	Difference and Functional Equations Differential equations Hypergeometric functions Mathematics Mathematics and Statistics Neighborhoods Ordinary Differential Equations Partial Differential Equations Polynomials Power series Studies
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	We specify the structure of the power series determining a solution of a Fuchsian second-order differential equation with polynomial coefficients in a neighborhood of zero. The power series is represented via hypergeometric functions of fractional order. The structure of the coefficients of the series is clarified.
ISSN:	0012-2661 1608-3083
DOI:	10.1134/S0012266111010034