Geodesic
On Salikhov's integral
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 77 (2016) no. 1, pp. 131-154 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We state a new interpolation problem, which we solve using Salikhov's integral. This was previously used in the theory of Diophantine approximations. We study the asymptotic behaviour of orthogonal polynomials related to this problem. 
@article{MMO_2016_77_1_a4,
     author = {V. N. Sorokin},
     title = {On {Salikhov's} integral},
     journal = {Trudy Moskovskogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {131--154},
     year = {2016},
     volume = {77},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MMO_2016_77_1_a4/}
}
TY  - JOUR
AU  - V. N. Sorokin
TI  - On Salikhov's integral
JO  - Trudy Moskovskogo matematičeskogo obŝestva
PY  - 2016
SP  - 131
EP  - 154
VL  - 77
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MMO_2016_77_1_a4/
LA  - ru
ID  - MMO_2016_77_1_a4
ER  - 
%0 Journal Article
%A V. N. Sorokin
%T On Salikhov's integral
%J Trudy Moskovskogo matematičeskogo obŝestva
%D 2016
%P 131-154
%V 77
%N 1
%U http://geodesic.mathdoc.fr/item/MMO_2016_77_1_a4/
%G ru
%F MMO_2016_77_1_a4
V. N. Sorokin. On Salikhov's integral. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 77 (2016) no. 1, pp. 131-154. http://geodesic.mathdoc.fr/item/MMO_2016_77_1_a4/

[1] Nikishin E. M., Sorokin V. N., Ratsionalnye approksimatsii i ortogonalnost, Nauka, M., 1988 | MR

[2] Mahler K., “Approximation der Exponentialfunction und des Logarithmus”, J. reine angew Math., 166 (1932), 118–150 | MR

[3] Feldman N. I., “Ob otsenke modulya lineinoi formy ot logarifmov nekotorykh algebraicheskikh chisel”, Matem. zametki, 2:3 (1967), 245–256 | Zbl

[4] Nikishin E. M., “O logarifmakh naturalnykh chisel”, Izv. AN SSSR. Ser. Matem., 43:6 (1979), 1319–1327 ; 44:4 (1980), 972 | MR | Zbl | MR | Zbl

[5] Sorokin V. N., “Otsenki mnogochlenov ot logarifmov nekotorykh ratsionalnykh chisel”, Fund. i prikl. matem., 11:6 (2005), 179–194

[6] Hata M., “Rational approximations to $\pi$ and some other numbers”, Acta arith., 63:4 (1993), 335–349 | MR | Zbl

[7] Sorokin V. N., Cherednikova E. N., “Nekotorye zamechaniya o priblizhenii logarifmov”, Vestnik Mosk. un–ta. Ser. 1. Matem., mekhan., 2007, no. 2, 21–26 | Zbl

[8] Rukhadze E. A., “Otsenka snizu priblizheniya $\ln 2$ ratsionalnymi chislami”, Vestnik Mosk. un–ta. Ser. 1. Matem., mekhan., 1987, no. 6, 25–29 | MR | Zbl

[9] Zudilin V. V., “Esse o merakh irratsionalnosti $\pi$ i drugikh logarifmov”, Chebyshevskii sbornik, 5:2 (2004), 49–65 | MR | Zbl

[10] Salikhov V. Kh., “O mere irratsionalnosti $\ln 3$”, Doklady RAN, 417:6 (2007), 753–755 | Zbl

[11] Landkof N. S., Osnovy sovremennoi teorii potentsiala, Nauka, M., 1966 | MR

[12] Gonchar A. A., Rakhmanov E. A., Sorokin V. N., “Ob approksimatsiyakh Ermita–Pade dlya sistem funktsii markovskogo tipa”, Matem. sb., 188:5 (1997), 33–58 | DOI | MR | Zbl