Geodesic
Strong asymptotics of the Hermite--Pad\'e approximants for a system of Stieltjes functions with Laguerre weight
Sbornik. Mathematics, Tome 196 (2005) no. 12, pp. 1815-1840

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The Hermite–Padé approximants with common denominator are considered for a pair of Stieltjes functions with weights $x^\alpha e^{-\beta_1x}$ and $x^\alpha e^{-\beta_2x}$, where $\alpha>-1$, $\beta_2>\beta_1>0$. On the basis of the method of the Riemann–Hilbert matrix problem the strong asymptotics of these approximants are found in the case $\beta_2/\beta_13+2\sqrt2$. The limiting distribution of the zeros of the denominators of the Hermite–Padé approximants is shown to be equal to the equilibrium measure of a certain Nikishin system. 
@article{SM_2005_196_12_a3,
     author = {V. G. Lysov},
     title = {Strong asymptotics of the {Hermite--Pad\'e} approximants for a system of {Stieltjes} functions with {Laguerre} weight},
     journal = {Sbornik. Mathematics},
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     volume = {196},
     number = {12},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2005_196_12_a3/}
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V. G. Lysov. Strong asymptotics of the Hermite--Pad\'e approximants for a system of Stieltjes functions with Laguerre weight. Sbornik. Mathematics, Tome 196 (2005) no. 12, pp. 1815-1840. http://geodesic.mathdoc.fr/item/SM_2005_196_12_a3/