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Regarding asymptotics of real zero $\alpha_n$ ($2/r_{2n-1}$ in OP's notation) of generalized Bessel polynomials (with an extra parameter $a$ specialized in the current case to $a=2$), see M.G. de Bruin, E.B. Saff’ and R.S. Varga, On the zeros of generalized Bessel polynomials, Proceedings A, 84 (l), 20, (1981). In theorem $7.3$ they state Obviously, $2/\...


1

The undergrad course I took which included B-splines spent a lot of time first on Bézier curves. You might not necessarily want to spend much time on them, but I think they can motivate a variant on method 1 by defining Bézier curves with de Casteljau's algorithm and B-spline curves with de Boor's algorithm. This assumes that you're at least as interested in ...


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