Abstract
It is shown that a modified version of the Stieltjes inversion formula for Nevanlinna-type functions, together with improved estimates of the Titchmarsh-Weyl function m(λ), constitute an effective approach to the problem of finding approximations to spectral functions for the case of - y″+q(x)y=λ y, 0<x<b≤∞.
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Atkinson, F.V. (1982). On the asymptotic behaviour of the Titchmarsh-Weyl m-coefficient and the spectral function for scalar second-order differential expressions. In: Everitt, W., Sleeman, B. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 964. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064985
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DOI: https://doi.org/10.1007/BFb0064985
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