Generalized Artin–Hasse and Iwasawa formulas for the Hilbert symbol in a higher local field

In the paper we consider the generalized Hilbert symbol in the cyclotomic extension of an absolutely unramified higher local field of characteristic 0 with perfect last residue field of characteristic $p>2$. We deduce the generalized Artin–Hasse and Iwasawa formulas from the explicit Kummer type Vostokov formula.