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In 1975 one of the coauthors, Ikebe, showed that the problem of computing the zeros of the regular Coulomb wave functions and their deriva- tives may be reformulated as the eigenvalue problem for innite matrices. Ap- proximation by truncation is justied but no error estimates are given there. The class of eigenvalue problems studied there turns out to be subsumed in a more general problem studied by Ikebe et al. in 1993, where an extremely accurate asymptotic error estimate is shown. In this paper, we apply this error formula to the former case to obtain error formulas in a closed, explicit form.

Error analysis for the computation of zeros of regular Coulomb wave function and its first derivative