incidentals about cardinal B-splines

25nov98 %
In an email, Bernhard Trebels (tu-darmstadt) observes numerically the following. Let $M_k$ be the centered cardinal B-spline of order $k$. Let $b_k := \sum_j (-1)^j M_k(1/2 + 2j)$, and $r_k := b_k/\sum_j(-1)^j M_k(j)$. %
Then $\lim_k r_{k+2}/r_k = 2$, with $r_{2s+1}/r_{2s-1} = 2$, for all $s$. %

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16may02 %
In an email, Scott Dale Gilberts guesses the following. With $f_n:= B(\cdot/n | 0:n)$, all $n$, there is, for each $n