Geodesic
Asymptotics of Diagonal Hermite--Pad\'e Polynomials for the Collection of Exponential Functions
Matematičeskie zametki, Tome 102 (2017) no. 2, pp. 302-315

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The asymptotics of diagonal Hermite–Padé polynomials of the first kind is studied for the system of exponential functions $\{e^{\lambda_pz}\}_{p=0}^k$, where $\lambda_0=0$ and the other $\lambda_p$ are the roots of the equation $\xi^k=1$. The theorems proved in the paper supplement the well-known results due to Borwein, Wielonsky, Stahl, Astaf'eva, and Starovoitov obtained for the case in which $\{\lambda_p\}_{p=0}^k$ are different real numbers.
Keywords: system of exponentials, Hermite–Padé approximants of the first kind, asymptotic equalities, Laplace method, saddle-point method. 
@article{MZM_2017_102_2_a11,
     author = {A. P. Starovoitov},
     title = {Asymptotics of {Diagonal} {Hermite--Pad\'e} {Polynomials} for the {Collection} of {Exponential} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {302--315},
     publisher = {mathdoc},
     volume = {102},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_102_2_a11/}
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A. P. Starovoitov. Asymptotics of Diagonal Hermite--Pad\'e Polynomials for the Collection of Exponential Functions. Matematičeskie zametki, Tome 102 (2017) no. 2, pp. 302-315. http://geodesic.mathdoc.fr/item/MZM_2017_102_2_a11/