Derangements and asymptotics of the Laplace transforms of large powers of a polynomial
نویسنده
چکیده
We use a probabilistic approach to produce sharp asymptotic estimates as n → ∞ for the Laplace transform of Pn, where P is a fixed complex polynomial. As a consequence we obtain a new elementary proof of a result of Askey-Gillis-Ismail-Offer-Rashed, [1, 3] in the combinatorial theory of derangements.
منابع مشابه
Derangements and asymptotics of Laplace transforms of polynomials
We describe the behavior as n → ∞ of the Laplace transforms of P, where P a fixed complex polynomial. As a consequence we obtain a new elementary proof of an result of Gillis-Ismail-Offer [2] in the combinatorial theory of derangements. 1 Statement of the main results The generalized derangement problem in combinatorics can be formulated as follows. Suppose X is a finite set and ∼ is an equival...
متن کامل2 1 Ja n 20 04 Derangements and asymptotics of Laplace transforms of polynomials
We describe the behavior as n → ∞ of the Laplace transforms of Pn, where P a fixed complex polynomial. As a consequence we obtain a new elementary proof of an result of Gillis-Ismail-Offer [2] in the combinatorial theory of derangements. 1 Statement of the main results The generalized derangement problem in combinatorics can be formulated as follows. Suppose X is a finite set and ∼ is an equiva...
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