7 problems

Let $f$ be a meromorphic function on a disk in $\mathbb{C}$, and let $[p/q]_f$ denote its Padé approximant of order $(p,q)$. The diagonal approximants are $[p/p]_f$. Baker–Gammel–W…

Let $P_{[p/q]}^{(c)}(x)$ denote the $[p/q]$ Padé approximant associated with the square-root expansion at $c$, and let $\beta_m^2(x,\sqrt{c})$ be the square biroot approximation. S…

Let $x=(x_1,\dots,x_n)$, let $T$ be a nonzero polynomial of order $m$, and let $P_T$ be the Padé matrix associated with the map sending $Q\in\mathbb{C}[x]_{\leq e}$ to the restrict…

Padé determinant-limit conjecture. The propagation amplitude is the infinite-size limit of the quotient of two amplitudes, each expressed as a determinant; specifically,

Ziętak's coefficient-sign conjecture. It is conjectured that $c_{k,i}<0$ for every $i\geq 1$, as long as the series for $x_k$ is not reduced to a finite series.

Laszkiewicz et al.'s convergence conjecture. If $k\ge m-1$ and $x_0$ lies in $L^{(\operatorname{Pad\acute{e}})}_p$, then

Let $F$ be a function holomorphic in a neighborhood of $\infty$. A diagonal $[n/n]$ Padé approximant is a rational function of the form described by the Padé approximation conditio…