  It turned out that the partial sums $g_n(z) = \sum_{k=0}^n \frac{(a_1)_k ...
(a_p)_k}{(b_1)_k ... (b_q)_k} \frac{z^k}{k!}$, of the generalized
hypergeometric series ${}_p F_q(a_1,...,a_p; b_1,...,b_q;z)$, with parameters
$a_j,b_l\in\mathbb{C}\backslash\{ 0,-1,-2,... \}$, are Sobolev orthogonal
polynomials. The corresponding monic polynomials $G_n(z)$ are polynomials of
$R_I$ type, and therefore they are related to biorthogonal rational functions.
Polynomials $g_n$ possess a differential equation (in $z$), and a recurrence
relation (in $n$). We study integral representations for $g_n$, and some other
their basic properties. Partial sums of arbitrary power series with non-zero
coefficients are shown to be also related to biorthogonal rational functions.
We obtain a relation of polynomials $g_n(z)$ to Jacobi-type pencils and their
associated polynomials.
