Abstract
By using methods of the potential theory there is studied an asymptotic behavior of simultaneous two-point Padé approximants of two Markov-type functions, one of which is holomorphic in a neighborhood of null, and the other one is holomorphic in the neighborhood of infinity. For special weights, there is obtained the Rodrigue's formula, and there is presented the asymptotics in terms of algebraic functions.
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Literature cited
A. A. Gonchar and E. A. Rakhmanov, “On the convergence of simultaneous Padé approximants for systems of functions of Markov type,” Proc. Matem. Inst., Akad. Nauk SSSR,157, 31–48 (1081).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 6, pp. 837–841, 1991.
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Sorokin, V.N. Simultaneous two-point Padé approximants of Markov functions. Ukr Math J 43, 784–788 (1991). https://doi.org/10.1007/BF01058948
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DOI: https://doi.org/10.1007/BF01058948