Let $f$ be an entire function of order $1$. Two questions:

1)Can one assert that the diagonal Padé approximants converge to $f$ (pointwise or uniformly over compacts of $\mathbb C$)?

2. if yes, can one estimate $|P_n(x)f(x)-Q_n(x)|$ in function of $n$ and $x$ (and $f$ of course), where $(P_n,Q_n)$ is the $[n,n]$-Padé approximants of $f$?

Thanks in advance.

Let $f$ be an entire function of order $1$. Two questions:

1. Can one assert that the diagonal Padé approximants converge to $f$ (pointwise or uniformly over compacts of $\mathbb C$)?

2. if yes, can one estimate $|P_n(x)f(x)-Q_n(x)|$ in function of $n$ and $x$ (and $f$ of course), where $(P_n,Q_n)$ is the $[n,n]$-Padé approximants of $f$?

Thanks in advance.