Geodesic
Asymptotics of Hermite--Pad\'e approximation of exponential functions with complex multipliers in the exponent
Problemy fiziki, matematiki i tehniki, no. 2 (2016), pp. 61-67

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Asymptotic properties of the diagonal Hermite–Padé approximants of type I for the system of exponentials $\{e^{\lambda_pz}\}^k_{p=0}$, in which $\lambda_0=0$, while the rest $\lambda_p$ are the roots of the equation $\xi^k=1$ are studied. The theorems complement known results of P. Borwein, F. Wielonsky, H. Stahl, A. V. Astafyeva, A. P. Starovoitov, obtained for the case, where the $\{\lambda_p\}^k_{p=0}$ — different real numbers.
Keywords: exponential system, asymptotic equality, Laplace's method, saddle point method.
Mots-clés : Hermite–Padé approximants 
@article{PFMT_2016_2_a9,
     author = {A. P. Starovoitov and G. N. Kazimirov and M. V. Sidorzov},
     title = {Asymptotics of {Hermite--Pad\'e} approximation of exponential functions with complex multipliers in the exponent},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {61--67},
     publisher = {mathdoc},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2016_2_a9/}
}
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A. P. Starovoitov; G. N. Kazimirov; M. V. Sidorzov. Asymptotics of Hermite--Pad\'e approximation of exponential functions with complex multipliers in the exponent. Problemy fiziki, matematiki i tehniki, no. 2 (2016), pp. 61-67. http://geodesic.mathdoc.fr/item/PFMT_2016_2_a9/