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Probabilistic proofs of asymptotic formulas for some classical polynomials

Published online by Cambridge University Press:  24 October 2008

Makoto Maejima  and
Walter Van Assche
Makoto Maejima
Affiliation:
Department of Mathematics, Keio University, Yokohama 223, Japan
Walter Van Assche
Affiliation:
Departement Wiskunde, Katholieke Universiteit Leuven, B-3030 Leuven, Belgium
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Extract

Recently Stadje [9] gave asymptotic formulas for some Bessel functions by using a probabilistic argument: some Bessel functions can be represented by the probability distribution of partial sums of symmetrized independent and identically distributed random variables (Feller [4], p. 149). Stadje used this idea and the local limit theorem, which is well known in probability theory.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 3 , May 1985 , pp. 499 - 510
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

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