scholarly journals Hayman Admissible Functions in Several Variables

10.37236/1132 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Bernhard Gittenberger ◽  
Johannes Mandlburger
Keyword(s):  
Asymptotic Expansion ◽  
Closure Properties ◽  
Several Variables ◽  
Class Of Functions ◽  
Admissible Functions

An alternative generalisation of Hayman's concept of admissible functions to functions in several variables is developed and a multivariate asymptotic expansion for the coefficients is proved. In contrast to existing generalisations of Hayman admissibility, most of the closure properties which are satisfied by Hayman's admissible functions can be shown to hold for this class of functions as well.

scholarly journals Certain Properties of a Class of Functions Defined by Means of a Generalized Differential Operator

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 174
Author(s):  
Matthew Olanrewaju Oluwayemi ◽  
Kaliappan Vijaya ◽  
Adriana Cătaş
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Closure Properties ◽  
Integral Means ◽  
Radius Of Starlikeness ◽  
Generalized Differential ◽  
The Relationship ◽  
Class Of Functions

In this article, we construct a new subclass of analytic functions involving a generalized differential operator and investigate certain properties including the radius of starlikeness, closure properties and integral means result for the class of analytic functions with negative coefficients. Further, the relationship between the results and some known results in literature are also established.

scholarly journals Some Algebraic Properties Of Asymptotic Power Series

1956 ◽  
Vol 8 ◽  
pp. 220-224
Author(s):  
T. E. Hull
Keyword(s):  
Asymptotic Expansion ◽  
Power Series ◽  
Asymptotic Power ◽  
Algebraic Properties ◽  
Image Position ◽  
The Right ◽  
The Given ◽  
Class Of Functions

1. Introduction. Let us consider all power series of the formIt was shown first by Borel (1) that to each such series there corresponds a non-empty class of functions such that each function in the class has the given series as its asymptotic expansion about z = 0, the expansion being valid in a sector of the right half z-plane with vertex at the origin.

scholarly journals On a New Class ofp-Valent Meromorphic Functions Defined in Conic Domains

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Mohammed Ali Alamri ◽  
Maslina Darus
Keyword(s):  
Hypergeometric Function ◽  
Meromorphic Functions ◽  
Starlike Functions ◽  
Closure Properties ◽  
New Class ◽  
Conic Domain ◽  
Class Of Functions

We define a new class of multivalent meromorphic functions using the generalised hypergeometric function. We derived this class related to conic domain. It is also shown that this new class of functions, under certain conditions, becomes a class of starlike functions. Some results on inclusion and closure properties are also derived.

scholarly journals Gérard-Sibuya's versus Majima's concept of asymptotic expansion in several variables

2001 ◽  
Vol 71 (1) ◽  
pp. 21-35 ◽  
Author(s):  
J. A. Hernández ◽  
J. Sanz
Keyword(s):  
Asymptotic Expansion ◽  
Holomorphic Function ◽  
The Other ◽  
Several Variables ◽  
Other Hand ◽  
The One ◽  
The Relationship ◽  
Derivatives Of

AbstractWe give an example of a holomorphic function, admitting Gérard-Sibuya asymptotic expansion on a polysector of Cn, and such that none of its derivatives admits such an expansion. This motivates the study of the relationship between the concepts of asymptotic expansion in several variables respectively given by Gérard-Sibuya and Majima. For a function f, Majima's notion is proved to be equivalent, on the one hand, to the existence of Gérard-Sibuya asymptotic expansion for f and its derivatives, and on the other hand, to the boundedness of the derivatives of f on bounded proper subpolysectors of S.

scholarly journals Admissible Functions and Asymptotics for Labelled Structures by Number of Components

10.37236/1258 ◽  
1996 ◽  
Vol 3 (1) ◽  
Author(s):  
Edward A. Bender ◽  
L. Bruce Richmond
Keyword(s):  
Limit Theorems ◽  
Local Limit ◽  
Singularity Analysis ◽  
Set Partition ◽  
Combinatorial Structures ◽  
Covering Problems ◽  
Several Variables ◽  
Exponential Generating Function ◽  
Local Limit Theorems ◽  
Admissible Functions

Let $a(n,k)$ denote the number of combinatorial structures of size $n$ with $k$ components. One often has $\sum_{n,k} a(n,k)x^ny^k/n! = \exp\{yC(x)\}$, where $C(x)$ is frequently the exponential generating function for connected structures. How does $a(n,k)$ behave as a function of $k$ when $n$ is large and $C(x)$ is entire or has large singularities on its circle of convergence? The Flajolet-Odlyzko singularity analysis does not directly apply in such cases. We extend some of Hayman's work on admissible functions of a single variable to functions of several variables. As applications, we obtain asymptotics and local limit theorems for several set partition problems, decomposition of vector spaces, tagged permutations, and various complete graph covering problems.

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