Abstract
The second member of the fourth Painlevé hierarchy is considered. Convergence of certain power asymptotic expansions in a neighborhood of zero is proved. New families of power asymptotic expansions are found. Computations are carried out using a computer algebra system. Reference to a code that can be used for computing the Gevrey order of the formal expansion of the solution to the second-order differential equation in a symbolic computation packet is given.
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Funding
This work was supported by the Russian Science Foundation, grant no. 19-71-10003, https://rscf.ru/en/project/19-71-10003/.
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Translated by A. Klimontovich
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Anoshin, V.I., Beketova, A.D., Parusnikova, A.V. et al. Convergence of Formal Solutions to the Second Member of the Fourth Painlevé Hierarchy in a Neighborhood of Zero. Comput. Math. and Math. Phys. 63, 86–95 (2023). https://doi.org/10.1134/S0965542523010049
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DOI: https://doi.org/10.1134/S0965542523010049