A family of hydrogen emission lines terminating at a fixed lower principal quantum number . In the nonrelativistic Bohr model, their inverse wavelengths are for integers . Holding fixed and increasing gives lines approaching the series limit . Reduced mass shifts the Rydberg constant, while additional interactions produce corrections to this gross spectral pattern.
The Brackett series consists of hydrogen spectral lines with final principal quantum number four and initial principal quantum number greater than four. The Rydberg formula gives . Its infrared wavelengths make these recombination lines less susceptible to interstellar extinction than optical Balmer series lines; quantitative use requires the appropriate effective recombination coefficient.

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The hydrogen spectral series refers to the specific wavelengths of light emitted or absorbed by hydrogen atoms when electrons transition between different energy levels. These transitions occur when an electron absorbs energy and moves to a higher energy level (excitation) or when it releases energy and falls back to a lower energy level (emission). The emitted or absorbed light appears in distinct spectral lines, grouped into series corresponding to different electron transitions.
Kind of a synonym for hydrogen emission spectrum not very clear if fine structure is considered by this term or not.
Formula discovered in 1885, was it the first set to have an empirical formula?