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An asymptotic formula for a two-point analogue of Jacobi polynomials. (English. Russian summary) Zbl 1284.41006

Russ. Math. Surv. 68, No. 4, 779-781 (2013); translation from Usp. Mat. Nauk 68, No. 4, 183-184 (2013).
The question of a complete description of the asymptotic behaviour of all the zeros of two-point Padé polynomials is still open (even for classical Padé approximations, this problem has not yet been completely solved).
In this paper the authors solve the problem for two-point Padé approximations of functions of the form \[ f(z)= (z- a_1)^\alpha(z- u_2)^{-\alpha}, \] where \(\alpha\in \mathbb{C}\setminus\mathbb{Q}\) and \(a_1\), \(a_2\) are two different points in \(\mathbb{C}\setminus\{0\}\).

MSC:

41A21 Padé approximation
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[1] А. И. Аптекарев, В. И. Буслаев, А. Мартинес-Финкельштейн, С. П. Суетин, УМН, 66:6(402) (2011), 37 – 122 · Zbl 1242.41014
[2] A. I. Aptekarev, M. L. Yattselev, arXiv: 1109.0332
[3] В. И. Буслаев, Матем. сб., 204:2 (2013), 39 – 72
[4] В. И. Буслаев, А. Мартинес-Финкельштейн, С. П. Суетин, Тр. МИАН, 279, МАИК, М., 2012, 31 – 58 · Zbl 1298.30028
[5] А. Мартинес-Финкельштейн, Е. А. Рахманов, С. П. Суетин, Матем. сб., 202:12 (2011), 113 – 136 · Zbl 1244.31001
[6] A. Martińez-Finkelshtein, E. A. Rakhmanov, S. P. Suetin, OPSFA/11, Contemp. Math., 578, Amer. Math. Soc., Providence, RI, 2012, 165 – 193 · Zbl 1250.00015
[7] А. Мартинес-Финкельштейн, Е. А. Рахманов, С. П. Суетин, УМН, 68:1(409) (2013), 197 – 198 · Zbl 1275.41019
[8] J. Nuttall, Constr. Approx., 2:1 (1986), 59 – 77 · Zbl 0585.41014
[9] H. Stahl, J. Approx. Theory, 91:2 (1997), 139 – 204 · Zbl 0896.41009
[10] С. П. Суетин, Матем. сб., 194:12 (2003), 63 – 92 · Zbl 1071.30001
[11] Г. Сегe\", Ортогональные многочлены, Физматгиз, М., 1962, 500 с. · Zbl 0100.28405
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