Recurrence Legendre polynomials
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2022), pp. 3-8
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The recurrence polynomials partly orthogonal with respect to Lebesgue measure on the segment symmetric with respect to the unit circle are studied. The limiting distribution of its zeros is obtained in terms of a meromorphic function on compact Riemann surface. The interpretation of the limiting measure is obtained in terms of equilibrium problems in the logarithmic potential theory.
@article{VMUMM_2022_6_a0,
     author = {V. N. Sorokin},
     title = {Recurrence {Legendre} polynomials},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {3--8},
     year = {2022},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2022_6_a0/}
}
TY  - JOUR
AU  - V. N. Sorokin
TI  - Recurrence Legendre polynomials
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2022
SP  - 3
EP  - 8
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2022_6_a0/
LA  - ru
ID  - VMUMM_2022_6_a0
ER  - 
%0 Journal Article
%A V. N. Sorokin
%T Recurrence Legendre polynomials
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2022
%P 3-8
%N 6
%U http://geodesic.mathdoc.fr/item/VMUMM_2022_6_a0/
%G ru
%F VMUMM_2022_6_a0
V. N. Sorokin. Recurrence Legendre polynomials. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2022), pp. 3-8. http://geodesic.mathdoc.fr/item/VMUMM_2022_6_a0/

[1] Sorokin V. N., “Approksimatsii Ermita–Pade funktsii Veilya i ee proizvodnoi dlya diskretnykh mer”, Matem. sb., 211:10 (2020), 139–156 | MR

[2] Sorokin V. N., “O mnogochlenakh sovmestnoi ortogonalnosti dlya diskretnykh mer Meiksnera”, Matem. sb., 201:10 (2010), 137–160

[3] Nikishin E. M., “O sovmestnykh approksimatsiyakh Pade”, Matem. sb., 113 (1980), 499–519

[4] Sorokin V. N., “O sovmestnykh dvukhtochechnykh approksimatsiyakh Pade markovskikh funktsii”, Ukr. matem. zhurn., 43:4 (1991), 584–588

[5] Markov A. A., “Deux demonstrations de la convergence de certains fractions continues”, Acta Math., 1895, 93–104 | DOI | MR

[6] Gonchar A. A., Rakhmanov E. A., “O zadache ravnovesiya dlya vektornykh potentsialov”, Uspekhi matem. nauk, 40:4 (1985), 155–156 | MR

[7] 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 | MR

[8] Angelesco A., “Sur deux extensions des fractions continues algebriques”, C.r. Acad. sci. Paris, 168 (1919), 262–265

[9] Nikishin E. M., “Asimptoticheskoe povedenie lineinykh form dlya sovmestnykh approksimatsii Pade”, Izv. vuzov. Matem., 1986, no. 2, 33–41 | MR

[10] Lysov V. G., “Silnaya asimptotika approksimatsii Ermita–Pade dlya sistemy stiltesovskikh funktsii s vesom Lagerra”, Matem. sb., 196:12 (2005), 99–122

[11] Sorokin V. N., “Ob asimptoticheskikh rezhimakh sovmestnykh mnogochlenov Meiksnera”, Preprinty IPM im. M.V. Keldysha, 2016, 046