  The aim of this work is to demonstrate various an interesting recursion
formulas, differential and integral operators, integration formulas, and
infinite summation for each of Horn's hypergeometric functions
$\mathrm{H}_{1}$, $\mathrm{H}_{2}$, $\mathrm{H}_{3}$, $\mathrm{H}_{4}$,
$\mathrm{H}_{5}$, $\mathrm{H}_{6}$ and $\mathrm{H}_{7}$ by the contiguous
relations of Horn's hypergeometric series. Some interesting different cases of
our main consequences are additionally constructed.
