On the Best Polynomial Approximations of Entire Transcendental Functions of Many Complex Variables in Some Banach Spaces

2015 ◽  
Vol 66 (12) ◽  
pp. 1793-1811 ◽  
Author(s):  
S. B. Vakarchuk ◽  
S. I. Zhir
Keyword(s):  
Banach Spaces ◽  
Complex Variables ◽  
Polynomial Approximations ◽  
Transcendental Functions

scholarly journals Research on Geometric Mappings in Complex Systems Analysis

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Yanyan Cui ◽  
Chaojun Wang ◽  
Sifeng Zhu
Keyword(s):  
Banach Spaces ◽  
Systems Analysis ◽  
Starlike Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Coefficient Estimates ◽  
Positive Real ◽  
Reinhardt Domains ◽  
Complex Order ◽  
Starlike Mappings

We mainly discuss the properties of a new subclass of starlike functions, namely, almost starlike functions of complex order λ, in one and several complex variables. We get the growth and distortion results for almost starlike functions of complex order λ. By the properties of functions with positive real parts and considering the zero of order k, we obtain the coefficient estimates for almost starlike functions of complex order λ on D. We also discuss the invariance of almost starlike mappings of complex order λ on Reinhardt domains and on the unit ball B in complex Banach spaces. The conclusions contain and generalize some known results.

scholarly journals Polynomial approximations on a polydisc

1972 ◽  
Vol 14 (2) ◽  
pp. 216-218
Author(s):  
Charles K. Chui
Keyword(s):  
Complex Variables ◽  
Open Unit ◽  
Polynomial Approximations ◽  
Distinguished Boundary ◽  
Image Position

Throughout this paper, we will use the terminologies and notations as in [4]. Thus, UN denotes the open unit polydisc in the space CN of N complex variables, TN the distinguished boundary of UN and .

Maclaurin Taylor Series for Transcendental Functions: A Graphing-Calculator View of Convergence

1999 ◽  
Vol 92 (9) ◽  
pp. 833-837
Author(s):  
Marvin E. Stick
Keyword(s):  
Polynomial Approximation ◽  
Taylor Series ◽  
Lower Order ◽  
Graphing Calculator ◽  
Transcendental Function ◽  
Maclaurin Series ◽  
Polynomial Approximations ◽  
Calculus Students ◽  
Transcendental Functions ◽  
Taylor Polynomials

Most calculus students can perform the manipulation necessary for a polynomial approximation of a transcendental function. However, many do not understand the underlying concept. Graphing-calculator technology can be used to bridge this gap between the concept of an interval of convergence for a series and polynomial approximations. Calculus-reform textbooks usually treat this topic by displaying lower-order Maclaurin series approximations to selected transcendental functions to encourage discussions of intervals of convergence. Some textbooks display lower-order Taylor polynomials for ln x expanded about x = 1. This article presents a way to examine the topic in more depth.

scholarly journals Banach spaces of functions analytic in a polydisc

1986 ◽  
Vol 9 (1) ◽  
pp. 39-46
Author(s):  
Leon M. Hall
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Analytic Functions ◽  
Hadamard Product ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Open Unit ◽  
Linear Functionals

This paper is concerned with functions of several complex variables analytic in the unit polydisc. Certain Banach spaces to which these functions might belong are defined and some relationships between them are developed. The space of linear functionals for the Banach space of functions analytic in the open unit polydisc and continuous on the unit torus is then described in terms of analytic functions using an extension of the Hadamard product.

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