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.

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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?