Coincidental spectral lines for the hydrogen atom

Asim Barut once, en passant, asked the question open-quotes For what transitions of the hydrogen atom do the spectral lines coincide?close quotes The answer is presented in this paper. In the spectrum of the hydrogen atom the coincidence of spectral lines is abundant and is governed by a four-parametric solution. The lowest energy for the first coincidence corresponds to n = 5, the Pfund series