2 problems

Let $f(z)=\sum_{j\geq 0}\gamma_j z^j$ be a formal power series, let $f_n(z)=\sum_{j=0}^{n}\gamma_j z^j$ be its partial sums, and set $s_n=f_n(z)$. For $k,n\in\mathbb{N}_0$, define…

A sequence transformation maps a sequence $\{z_n\}_n$ to a sequence $\{w_n\}_n$. For the Jacobi-Stirling numbers of the second kind $\operatorname{JS}(n,k;z)$ and the Jacobi-Stirli…