Uniqueness of the solutions of the Hermite – Pade problems
https://doi.org/10.29235/1561-2430-2019-55-4-445-456
Abstract
New concepts are introduced in the present work. They are a quite normal index and a quite perfect system of functions. Using these concepts, the uniqueness criterion for solution of two Hermite – Pade problems is proved, the explicit determinant representations of type I and II Hermite – Padé polynomials for an arbitrary system of power series are obtained. The results obtained complement and generalize the well-known result in the theory of Hermite – Padé approximations.
About the Authors
A. P. Staravoitov
Francisk Scorina Gomel State University
Russian Federation
Russian Federation
Aleksandr P. Staravoitov – Dr. Sc. (Physics and Mathematics), Professor.
104, Sovetskaya Str., 246019, Gomel
N. V. Ryabchenko
Francisk Scorina Gomel State University
Russian Federation
Russian Federation
Nataliya V. Ryabchenko – Senior Lecturer.
104, Sovetskaya Str., 246019, Gomel
References
1. Nikishin E. M., Sorokin V. N. Rational Approximations and Orthogonality. Moscow, Nauka Publ., 1988. 256 p. (in Russian).
2. Baker Jr. G. A., Graves-Morris P. Pad´e Approximants. 2nd ed. Cambridge University Press, 1996. https://doi. org/10.1017/CBO9780511530074
3. Stahl H. Asymptotics for quadratic Hermite-Padé polynomals associated with the exponential function. Electronic Transactions on Numerical Analysis, 2002, no. 14, pp. 193–220.
4. Aptekarev A. I., Buslaev V. I., Mart´ınez-Finkelshtein A., and Suetin S. P. Pad´e approximants, continued fractions, and orthogonal polynomials. Russian Mathematical Surveys, 2011, vol. 66, no. 6, pp. 1049–1131. https://doi.org/10.1070/ rm2011v066n06abeh004770
5. Hermite C. Sur la function exponentielle. Comptes Rendus de l'Académie des Sciences, 1873, vol. 77, pp. 18–293.
6. Hermite C. Sur la generalisation des fractions continues algebriques. Annali di Matematica Pura ed Applicata, 1893, vol. 21, no. 1, pp. 289–308. https://doi.org/10.1007/bf02420446
Review
Views: 913
Email this article 