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Alexandre Eremenko
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$$|a_n|\sim\frac{\Gamma(n/2+1)}{\Gamma(n+1)}\exp\frac{2\sqrt{2n}}{2}.$$ Ref. Szego, Orthogonal polynomials, AMS. 1959, formula (8.23.4), see also (9.2.9).

Alexandre Eremenko
  • 91.8k
  • 9
  • 259
  • 429