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PFMT, 2017, Issue 2(31), Pages 69–74 (Mi pfmt505)  

MATHEMATICS

Asymptotics of Hermite–Padé degenerate hypergeometric functions

M. V. Sidortsov, A. A. Drapeza, A. P. Starovoitov

F. Sсorina Gomel State University

Abstract: 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 $\mathbb{C}\setminus\{0,-1,-2,…\}$ 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.

Full text: PDF file (353 kB)
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UDC: 517.538.52+517.538.53
Received: 09.03.2017

Citation: M. V. Sidortsov, A. A. Drapeza, A. P. Starovoitov, “Asymptotics of Hermite–Padé degenerate hypergeometric functions”, PFMT, 2017, no. 2(31), 69–74

Citation in format AMSBIB
\Bibitem{SidDraSta17}
\by M.~V.~Sidortsov, A.~A.~Drapeza, A.~P.~Starovoitov
\paper Asymptotics of Hermite--Pad\'e degenerate hypergeometric functions
\jour PFMT
\yr 2017
\issue 2(31)
\pages 69--74
\mathnet{http://mi.mathnet.ru/pfmt505}


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