The generalized order and the generalized type of an entire function in terms of the best approximation

TL;DR

This paper investigates how the generalized order and type of entire functions relate to the speed of their best polynomial approximations in the unit disk, extending previous mathematical results.

Contribution

It establishes new relations linking generalized order and type of entire functions to their best approximation sequences, generalizing prior work.

Findings

Derived formulas connecting generalized order and type with approximation speed

Extended previous results by Reddy, Sato, Ibragimov, and others

Provided a theoretical framework for analyzing entire functions via approximation

Abstract

The paper explores connection between the generalized order and the generalized type of an entire function and the speed of the best polynomial approximation in the unit disk. The relations which define the generalized order and the generalized type of an entire function through the sequence of its best approximations, have been found. The results were obtained by generalization previous results of A.R. Reddy, D. Sato, I.I. Ibragimov and N. I. Shyhaliev, S. B. Vakarchyk, R. Mamadov.