## 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 $$\mathbb{C}\setminus\{0\}$$.