  The three Mn I lines at 17325, 17339 and 17349 \AA~are among the 25 strongest
lines ($\log(gf)>0.5$) in the H-band. They are all heavily broadened due to
hyperfine structure and the profiles of these lines have so far not been
understood. Earlier studies of these lines even suggested that they were
blended. In this work, the profiles of these three infra-red (IR) lines have
been studied theoretically and compared to experimental spectra to assist in
the complete understanding of the solar spectrum in the IR. It is shown that
the structure of these lines can not be described in the conventional way by
the diagonal $A$ and $B$ hyperfine interaction constants. The off-diagonal
hyperfine interaction not only has large impact on the energies of the
hyperfine levels, but also introduces a large intensity redistribution among
the hyperfine lines, changing the line profiles dramatically. By performing
large-scale calculations of the diagonal and off-diagonal hyperfine interaction
and $gf$-values between the upper and lower hyperfine levels and using a
semi-empirical fitting procedure, agreement between our synthetic and
experimental spectra was achieved. Furthermore, we compare our results with
observations of stellar spectra. The spectra of the Sun and the K1.5 III red
giant star Arcturus were modelled in the relevant region, $1.73-1.74$ $\mu$m
using our theoretically predicted $gf$-values and energies for each individual
hyperfine line. Satisfactory fits were obtained and clear improvements were
found using our new data compared with the old available Mn I data. A complete
list of energies and $gf$-values for all the $3d^54s({^7S})4d$ e$^{6}$D $-$
$3d^54s({^7S})4f$ w$^{6}$F hyperfine lines are available as supplementary
material online, whereas only the stronger lines are presented and discussed in
detail in this paper.
