Geodesic
On asymptotics of solution of nonlinear difference equation of convolution type
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 5th International Conference "Dynamical Systems and Computer Science: Theory and Applications" (DYSC 2023). Irkutsk, September 18-23, 2023, Tome 234 (2024), pp. 21-26

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Nonlinear difference equations appear in many problems of probability theory, computer science, and combinatorics. In this paper, a nonlinear difference equation of the convolution type with parameters is considered. Asymptotics of solutions of such equations are used for the enumeration of labeled connected graphs. To obtain the asymptotics, we apply Bender's theorem for the coefficients of formal power series.
Keywords: difference equation, nonlinearity, asymptotics, labeled graph, enumeration
Mots-clés : convolution 
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     author = {V. A. Voblyi},
     title = {On asymptotics of solution of nonlinear difference equation of convolution type},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {21--26},
     publisher = {mathdoc},
     volume = {234},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2024_234_a2/}
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V. A. Voblyi. On asymptotics of solution of nonlinear difference equation of convolution type. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 5th International Conference "Dynamical Systems and Computer Science: Theory and Applications" (DYSC 2023). Irkutsk, September 18-23, 2023, Tome 234 (2024), pp. 21-26. http://geodesic.mathdoc.fr/item/INTO_2024_234_a2/