This is an interesting and well-written paper on a highly theoretical subject: deriving an estimate for &ggr;_n(&agr;), which is defined as follows: &ggr;_n(&agr;) = sup{‖ p′ ‖/‖p ‖ for p in P_n}, where P_n is the set of all complex polynomials with degree not exceeding n, and ‖ . ‖ is the weighted L²-norm with Laguerre weight t^&agr;e^-t, for &agr; > -1.

Section 1 highlights the importance of the problem, and reviews existing results. The complementarity of past efforts is emphasized, and methods of work employed are commented on.

Section 2 presents the single contribution of this paper, a theorem stating that &ggr;_n(&agr;)/n → (j_(&agr;-1)/2)-1, as n → ∞, where j_v is the first positive zero of the Bessel function of the first kind of order v.

Section 3 states and proves seven lemmas essential for “building” a proof for the theorem. These lemmas deal with various concepts, for example Pollaczek polynomials and Bessel functions, and thus may find application in other problems.

The paper concludes with an elegant proof of the new theorem, employing the given lemmas, as well as standard results from complex analysis.

In conclusion, this is a very well-structured paper, where the given proof is nicely divided into substantial lemmas. The author also includes many interesting remarks on the methodologies and methods/techniques employed (or not employed). This is an excellent example of how to write a good paper; I recommend it as reading material for all graduate students in the field of approximation theory.