A Neumann series of Bessel functions representation for solutions of Sturm–Liouville equations

• DOI: 10.1007/s10092-018-0254-7
• Publication Date: 2018-02-19T11:38:04Z
• Authors: Vladislav V. Krav...; Sergii M. Torba
• Keywords: Truncation (statistics); Sturm–Liouville theory; Representation

Some typos corrected<br/>A Neumann series of Bessel functions (NSBF) representation for solutions of Sturm-Liouville equations and for their derivatives is obtained. The representation possesses an attractive feature for applications: for all real values of the spectral parameter $��$ the difference between the exact solution and the approximate one (the truncated NSBF) depends on $N$ (the truncation parameter) and the coefficients of the equation and does not depend on $��$. A similar result is valid when $��\in\mathbb{C}$ belongs to a strip $|Im��|<br/>