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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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