Mittag-Leffler series for generating continuum sum?

[bo198214]

The function \( \frac{1}{1 - w} \) is single-valued and analytic on G [described as "the domain G bounded by the segment u >= 1, v = 0 (the part of the real axis going from 1 to \( \infty \)", which sounds like the Mittag-Leffler star of that function], and hence, by Runge's theorem (Theorem 3.5) there exists a sequence of polynomials

\( P_n(w) = c_0^{(n)} + c_1^{(n)} w + ... + c_{k_n}^{(n)} w^{k_n} \)

such that

\( lim_{n \rightarrow \infty} P_n(w) = \frac{1}{1 - w} \)

where the convergence is uniform inside G, in particular on the compact set \( E(F, L) \subset G \).

yes thats the same as in the 1967 edition.
There you will also find Runge's theorem.