Geodesic
On Multiple Orthogonal Polynomials for Three Meixner Measures
Informatics and Automation, Complex analysis and its applications, Tome 298 (2017), pp. 315-337.

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Multiple orthogonal polynomials for three discrete Meixner measures with identical exponential decay at infinity are studied. These polynomials are the denominators of the type II Hermite–Padé approximants to some hypergeometric functions. The limit distribution of zeros of such polynomials scaled in a certain way is described in terms of equilibrium logarithmic potentials and in terms of algebraic curves.
Keywords: Meixner polynomials, Angelesco and Nikishin systems, Riemann surfaces, algebraic functions, equilibrium logarithmic potentials. 
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V. N. Sorokin. On Multiple Orthogonal Polynomials for Three Meixner Measures. Informatics and Automation, Complex analysis and its applications, Tome 298 (2017), pp. 315-337. http://geodesic.mathdoc.fr/item/TRSPY_2017_298_a17/

[1] Arvesú J., Coussement J., Van Assche W., “Some discrete multiple orthogonal polynomials”, J. Comput. Appl. Math., 153 (2003), 19–45 | DOI | MR | Zbl

[2] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii: Funktsii Besselya, funktsii parabolicheskogo tsilindra, ortogonalnye mnogochleny, Nauka, M., 1966 | MR

[3] Gonchar A. A., Rakhmanov E. A., “O skhodimosti sovmestnykh approksimatsii Pade dlya sistem funktsii markovskogo tipa”, Tr. MIAN, 157, 1981, 31–48 | Zbl

[4] Gonchar A. A., Rakhmanov E. A., “Ravnovesnaya mera i raspredelenie nulei ekstremalnykh mnogochlenov”, Mat. sb., 125:1 (1984), 117–127 | MR

[5] Gonchar A. A., Rakhmanov E. A., “O zadache ravnovesiya dlya vektornykh potentsialov”, UMN, 40:4 (1985), 155–156 | MR | Zbl

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

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

[8] Martines-Finkelshtein A., Rakhmanov E. A., Suetin S. P., “Variatsiya ravnovesnoi energii i $S$-svoistvo statsionarnogo kompakta”, Mat. sb., 202:12 (2011), 113–136 | DOI | MR

[9] Nikishin E. M., “O sovmestnykh approksimatsiyakh Pade”, Mat. sb., 113:4 (1980), 499–519 | MR | Zbl

[10] Nikishin E. M., “Ob asimptotike lineinykh form dlya sovmestnykh approksimatsii Pade”, Izv. vuzov. Matematika, 1986, no. 2, 33–41 | MR | Zbl

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

[12] Rakhmanov E. A., “Ob asimptoticheskikh svoistvakh mnogochlenov, ortogonalnykh na veschestvennoi osi”, Mat. sb., 119:2 (1982), 163–203 | MR | Zbl

[13] Rakhmanov E. A., “Ravnovesnaya mera i raspredelenie nulei ekstremalnykh mnogochlenov diskretnoi peremennoi”, Mat. sb., 187:8 (1996), 109–124 | DOI | MR | Zbl

[14] Sorokin V. N., “O mnogochlenakh sovmestnoi ortogonalnosti dlya diskretnykh mer Meiksnera”, Mat. sb., 201:10 (2010), 137–160 | DOI | Zbl

[15] Sorokin V. N., Ob asimptoticheskikh rezhimakh sovmestnykh mnogochlenov Meiksnera, Preprinty IPM im. M. V. Keldysha, 2016, 32 pp.