Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 3, pp. 525-530
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A. V. Prokhorov. Inequalities for Bessel functions of imaginary argument. Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 3, pp. 525-530. http://geodesic.mathdoc.fr/item/TVP_1968_13_3_a15/
@article{TVP_1968_13_3_a15,
author = {A. V. Prokhorov},
title = {Inequalities for {Bessel} functions of imaginary argument},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {525--530},
year = {1968},
volume = {13},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1968_13_3_a15/}
}
TY - JOUR
AU - A. V. Prokhorov
TI - Inequalities for Bessel functions of imaginary argument
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1968
SP - 525
EP - 530
VL - 13
IS - 3
UR - http://geodesic.mathdoc.fr/item/TVP_1968_13_3_a15/
LA - ru
ID - TVP_1968_13_3_a15
ER -
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%A A. V. Prokhorov
%T Inequalities for Bessel functions of imaginary argument
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1968
%P 525-530
%V 13
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_1968_13_3_a15/
%G ru
%F TVP_1968_13_3_a15
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.
