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Hermite—Padé Approximants of the Mittag-Leffler Functions

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Abstract

The convergence rate of type II Hermite–Padé approximants for a system of degenerate hypergeometric functions {1F1(1, γ; λjz)} k j=1 is found in the case when the numbers {λj} k j=1 are the roots of the equation λk = 1 or real numbers and \(\gamma\in\mathbb{C}\;\backslash\left\{0,-1,-2,...\right\}\). More general statements are obtained for approximants of this type (including nondiagonal ones) in the case of k = 2. The theorems proved in the paper complement and generalize the results obtained earlier by other authors.

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  1. Francisk Skorina Gomel State University, Savetskaya vul. 104, Gomel, 246019, Belarus

    A. P. Starovoitov

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Original Russian Text © A.P. Starovoitov, 2018, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2018, Vol. 301, pp. 241–258.

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Starovoitov, A.P. Hermite—Padé Approximants of the Mittag-Leffler Functions. Proc. Steklov Inst. Math. 301, 228–244 (2018). https://doi.org/10.1134/S0081543818040181

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