This article is cited in 4 papers

Short Communications

Inequalities for Bessel functions of imaginary argument

A. V. Prokhorov

M. V. Lomonosov Moscow State University

Abstract: Using probabilistic arguments (the method of conjugate distributions and a local limit theorem), we prove two-sided inequality (9) for modified Bessel functions $I_n(z)$ with integer $n\ge0$. The inequalities obtained are very useful, for example, in estimation of probabilities of large deviations in spaces of high dimensionality.

Received: 23.04.1968

 English version: Theory of Probability and its Applications, 1968, 13:3, 496–501

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