Geodesic
Multipoint Hermite--Pad\'e Approximations for Beta Functions
Matematičeskie zametki, Tome 87 (2010) no. 2, pp. 217-232

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We construct multipoint Hermite–Padé approximations for two beta functions generating the Nikishin system with infinite discrete measures and unbounded supports. The asymptotic behavior of the approximants is studied. The result is interpreted in terms of the vector equilibrium problem in logarithmic potential theory in the presence of an external field and constraints on measure.
Keywords: Hermite–Padé approximation, beta function, pole of a meromorphic function, logarithmic potential, Mittag–Leffler expansion, Riemann sphere
Mots-clés : Laurent series, Cauchy transform, Rodrigues formula, Lebesgue measure. 
@article{MZM_2010_87_2_a4,
     author = {A. A. Kandayan and V. N. Sorokin},
     title = {Multipoint {Hermite--Pad\'e} {Approximations} for {Beta} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {217--232},
     publisher = {mathdoc},
     volume = {87},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_87_2_a4/}
}
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A. A. Kandayan; V. N. Sorokin. Multipoint Hermite--Pad\'e Approximations for Beta Functions. Matematičeskie zametki, Tome 87 (2010) no. 2, pp. 217-232. http://geodesic.mathdoc.fr/item/MZM_2010_87_2_a4/