Meneghini, Claudio Painlevé’s theorem extended. (English) Zbl 1052.34081 Rend. Semin. Mat. Univ. Padova 108, 93-96 (2002). The author proves a certain refinement of the so-called Painlevé’s determinateness theorem of E. Hille [Ordinary differential equations in the complex domain. New York etc.: John Wiley & Sons, a Wiley-Interscience Publication (1976; Zbl 0343.34007), Theorem 3.3.1] concerning the \(C_0\)-continuability to singular points of a holomorphic solution \(W(.)\) to the differential equation \(W'(z)=F(W(z),z)\) in the complex domain. Reviewer: Stefan Mirică (Bucuresti) MSC: 34M05 Entire and meromorphic solutions to ordinary differential equations in the complex domain 34M35 Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms Keywords:differential equation in the complex domain; continuation of solution; Riemann domain; algebraic set Citations:Zbl 0343.34007 × Cite Format Result Cite Review PDF Full Text: arXiv EuDML References: [1] E. GIUSTI, Analisi Matematica, vol. 2, Bollati Boringhieri, 1989. [2] ROBERT C. GUNNING - HUGO ROSSI, Analytic functions of several complex variables, Prentice Hall, 1965. Zbl0141.08601 MR180696 · Zbl 0141.08601 [3] EINAR HILLE, Ordinary differential equations in the complex domain, John Wiley & sons, 1976. Zbl0343.34007 MR499382 · Zbl 0343.34007 [4] E. L. INCE, Ordinary differential equations, Dover, 1956 (originally published in 1926). Zbl0063.02971 MR10757 JFM53.0399.07 · Zbl 0063.02971 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.