Abstract
A new representation for solutions of linear higher order ordinary differential equations with a spectral parameter is obtained in terms of Neumann series of Bessel functions. The result is based on a Fourier-Legendre series representation for the Borel transform of the solution with respect to the spectral parameter. Estimates for the coefficients and for the convergence of the representation are derived. Numerical illustrations of the applicability of the obtained formulae are presented.
V. V. Kravchenko on sabbatical leave from Cinvestav, Mexico.
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Research was supported by CONACYT, Mexico via the project 284470.
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Gómez, F.A., Kravchenko, V.V. (2019). On Transmutation Operators and Neumann Series of Bessel Functions Representations for Solutions of Linear Higher Order Differential Equations. In: Karapetyants, A., Kravchenko, V., Liflyand, E. (eds) Modern Methods in Operator Theory and Harmonic Analysis. OTHA 2018. Springer Proceedings in Mathematics & Statistics, vol 291. Springer, Cham. https://doi.org/10.1007/978-3-030-26748-3_21
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