$\newcommand{\ch}{\mathrm{ch}}$We define the Chern character of $E$ a rank $r$ locally free sheaf on a nonsingular projective variety as $$ \ch(E) = \sum_{i=1}^r e^{a_i} $$ where the $a_i$ are formal symbols arising from the Chern polynomial $ c_t(E) = \prod_{i=1}^r (1+a_it)$. The Chern character can be given more explicitly by $$ \ch(E) = r + c_1 + \frac{1}{2}(c_1^2 - 2c_2) + \frac{1}{6}(c_1^3-3c_1c_2 + 3c_3) + \cdots $$ where $r=\mathrm{rk}(E)$, $c_i = c_i(E)$ are the $i$th Chern classes, and $c_i =0$ if $i > r$.
I've seen the term $i$th Chern character denoted $\ch_i$ being used and I was wondering what the definition of it is? I've searched through a few books but have had no luck, though I've seen things like $\ch = (\ch_0, \dots, \ch_n)$ written down. My guess would be that $\ch_i(E)$ is the sum of all of the $i$th Chern classes $c_i$ appearing in the formula for $\ch(E)$ - would this be the correct interpretation?