Geodesic
Asymptotics of Hermite--Pad\'e degenerate hypergeometric functions
Problemy fiziki, matematiki i tehniki, no. 2 (2017), pp. 69-74

Voir la notice de l'article provenant de la source Math-Net.Ru

The asymptotic behavior of diagonal Hermite–Padé polynomials and diagonal Hermite–Padé approximations of type II for the system $\{_1F_1(1,\gamma;\lambda_jz)\}_{j=1}^k$, consisting of degenerate hypergeometric functions in which while the rest $\{\lambda_j\}_{j=1}^k$ are the roots of the equation $\lambda^k=1$, $\gamma$ — is a complex number belonging to the set $\mathbb{C}\setminus\{0,-1,-2,\dots\}$ was stated. The theorems complement known results of H. Padé, D. Braess, A.I. Aptekarev, H. Stahl, F. Wielonsky, W. Van Assche, A. B. J. Kuijlaars, A.P. Starovoitov, obtained for the case, where the $\{\lambda_p\}_{p=0}^k$ — different real numbers.
Keywords: Hermite integrals, Hermite–Padé polynomials, Hermite–Padé approximations, asymptotic equality, degenerate hypergeometric functions. 
@article{PFMT_2017_2_a11,
     author = {M. V. Sidortsov and A. A. Drapeza and A. P. Starovoitov},
     title = {Asymptotics of {Hermite--Pad\'e} degenerate hypergeometric functions},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {69--74},
     publisher = {mathdoc},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2017_2_a11/}
}
TY  - JOUR
AU  - M. V. Sidortsov
AU  - A. A. Drapeza
AU  - A. P. Starovoitov
TI  - Asymptotics of Hermite--Pad\'e degenerate hypergeometric functions
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2017
SP  - 69
EP  - 74
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2017_2_a11/
LA  - ru
ID  - PFMT_2017_2_a11
ER  - 
%0 Journal Article
%A M. V. Sidortsov
%A A. A. Drapeza
%A A. P. Starovoitov
%T Asymptotics of Hermite--Pad\'e degenerate hypergeometric functions
%J Problemy fiziki, matematiki i tehniki
%D 2017
%P 69-74
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2017_2_a11/
%G ru
%F PFMT_2017_2_a11
M. V. Sidortsov; A. A. Drapeza; A. P. Starovoitov. Asymptotics of Hermite--Pad\'e degenerate hypergeometric functions. Problemy fiziki, matematiki i tehniki, no. 2 (2017), pp. 69-74. http://geodesic.mathdoc.fr/item/PFMT_2017_2_a11/