Geodesic
Computation of the $\varepsilon$ entropy of the space of continuous functions with the Hausdorff metric
Matematičeskie zametki, Tome 21 (1977) no. 1, pp. 39-50.

Voir la notice de l'article provenant de la source Math-Net.Ru

The number $K_{p,q}$, i.e., the number of $(p,q)$ corridors of closed domains which are convex in the vertical direction, consist of elementary squares of the integral lattice, are situated within a rectangle of the size $q\times p$, and completely cover the side of length $p$ of this rectangle under projection is computed. The asymptotic $(K_{p,q}/q^2)^{1/p}\to\lambda$, as $p,q\to\infty$, where $\lambda=0,\!3644255\dots$ is the maximum root of the equation $_1F_1(-1/2-1/(16\lambda),1/2,1/(4\lambda))=0$, $_1F_1$ being the confluence hypergeometric function, is established. These results allow us to compute the $\varepsilon$ entropy of the space of continuous functions with the Hausdorff metric. 
@article{MZM_1977_21_1_a4,
     author = {A. A. Panov},
     title = {Computation of the $\varepsilon$ entropy of the space of continuous functions with the {Hausdorff} metric},
     journal = {Matemati\v{c}eskie zametki},
     pages = {39--50},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_21_1_a4/}
}
TY  - JOUR
AU  - A. A. Panov
TI  - Computation of the $\varepsilon$ entropy of the space of continuous functions with the Hausdorff metric
JO  - Matematičeskie zametki
PY  - 1977
SP  - 39
EP  - 50
VL  - 21
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1977_21_1_a4/
LA  - ru
ID  - MZM_1977_21_1_a4
ER  - 
%0 Journal Article
%A A. A. Panov
%T Computation of the $\varepsilon$ entropy of the space of continuous functions with the Hausdorff metric
%J Matematičeskie zametki
%D 1977
%P 39-50
%V 21
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1977_21_1_a4/
%G ru
%F MZM_1977_21_1_a4
A. A. Panov. Computation of the $\varepsilon$ entropy of the space of continuous functions with the Hausdorff metric. Matematičeskie zametki, Tome 21 (1977) no. 1, pp. 39-50. http://geodesic.mathdoc.fr/item/MZM_1977_21_1_a4/