Komlov, A. V.; Suetin, S. P. 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 \(\mathbb{C}\setminus\{0\}\). Reviewer: Francisco Pérez Acosta (La Laguna) Cited in 2 Documents MSC: 41A21 Padé approximation Keywords:two-point Padé approximants; Jacobi polynomials; asymptotic behaviour PDFBibTeX XMLCite \textit{A. V. Komlov} and \textit{S. P. Suetin}, Russ. Math. Surv. 68, No. 4, 779--781 (2013; Zbl 1284.41006); translation from Usp. Mat. Nauk 68, No. 4, 183--184 (2013) Full Text: DOI References: [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.