(p, q)-Growth of Meromorphic Functions and the Newton-Pade Approximant

  • Mohammed Harfaoui University Hassan II Mohammedia, Laboratory of Mathematics, Criptography and Mechanical F. S. T., BP 146, Mohammedia 20650, Morocco.
  • Loubna Lakhmaili University Hassan II Mohammedia, Laboratory of Mathematics, Criptography and Mechanical F. S. T., BP 146, Mohammedia 20650, Morocco.
  • Abdellah Mourassil University Hassan II Mohammedia, Laboratory of Mathematics, Criptography and Mechanical F. S. T., BP 146, Mohammedia 20650, Morocco.
Keywords: Generalized the growth, meromorphic functions, Pad-approximants, best rational approximation, (p, q)-order and (p, q)-type, logarithmic capacity

Abstract

In this paper, we have considered the generalized growth ((p, q)-order and (p, q)-type) in term of coefficient of the developpement pnn given by

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in the (n, n)-th Newton-pade approximant of meromorphic function. We use these results to study the relationship betwen the degree of convergence in capacity of interpolating functions and information on the degree of convergence of best rational approximation on a compact of C (in the supremum norm). We will also show that the order of meromorphic functions puts an upper bound on the degree of convergence.

Published
2020-02-12
How to Cite
Harfaoui, M., Lakhmaili, L., & Mourassil, A. (2020). (p, q)-Growth of Meromorphic Functions and the Newton-Pade Approximant. Theory and Applications of Mathematical Science Vol. 2, 93-102. Retrieved from https://stm1.bookpi.org/index.php/tams-v2/article/view/1025
Issue
Theory and Applications of Mathematical Science Vol. 2
Section
Chapters