  The paper deals with particular classes of $q\times q$ matrix-valued
functions which are holomorphic in $\mathbb{C}\setminus[\alpha,+\infty)$, where
$\alpha$ is an arbitrary real number. These classes are generalizations of
classes of holomorphic complex-valued functions studied by Kats and Krein [17]
and by Krein and Nudelman [19]. The functions are closely related to truncated
matricial Stieltjes problems on the interval $[\alpha,+\infty)$.
Characterizations of these classes via integral representations are presented.
Particular emphasis is placed on the discussion of the Moore-Penrose inverse of
these matrix-valued functions.
