A Simple Pole in Ithaca, NY

2016 ◽  
Vol 9 (0) ◽  
Author(s):  
Daniel W. Stroock
Keyword(s):  
Simple Pole

scholarly journals Flexible simple-pole expansion of distribution functions

1997 ◽  
Vol 4 (10) ◽  
pp. 3469-3476 ◽  
Author(s):  
T. Löfgren ◽  
H. Gunell
Keyword(s):  
Distribution Functions ◽  
Simple Pole

scholarly journals Extremal Problems for Functions Starlike in the Exterior of the Unit Circle

1962 ◽  
Vol 14 ◽  
pp. 540-551 ◽  
Author(s):  
W. C. Royster
Keyword(s):  
Unit Circle ◽  
Analytic Functions ◽  
Upper Bounds ◽  
Extremal Problems ◽  
Simple Pole ◽  
Image Position ◽  
Inverse Functions ◽  
Variational Formulas

Let Σ represent the class of analytic functions(1)which are regular, except for a simple pole at infinity, and univalent in |z| > 1 and map |z| > 1 onto a domain whose complement is starlike with respect to the origin. Further let Σ- 1 be the class of inverse functions of Σ which at w = ∞ have the expansion(2).In this paper we develop variational formulas for functions of the classes Σ and Σ- 1 and obtain certain properties of functions that extremalize some rather general functionals pertaining to these classes. In particular, we obtain precise upper bounds for |b2| and |b3|. Precise upper bounds for |b1|, |b2| and |b3| are given by Springer (8) for the general univalent case, provided b0 =0.

scholarly journals Remarks on the Elliptic Case of the Mapping Theorem for Simply-Connected Riemann Surfaces

1955 ◽  
Vol 9 ◽  
pp. 17-20 ◽  
Author(s):  
Maurice Heins
Keyword(s):  
Riemann Surface ◽  
Meromorphic Function ◽  
Riemann Surfaces ◽  
Simple Pole ◽  
Conformal Map ◽  
Elliptic Case ◽  
Extended Plane ◽  
Simply Connected ◽  
Conformal Equivalence

It is well-known that the conformal equivalence of a compact simply-connected Riemann surface to the extended plane is readily established once it is shown that given a local uniformizer t(p) which carries a given point p0 of the surface into 0, there exists a function u harmonic on the surface save at p0 which admits near p0 a representation of the form(α complex 0; h harmonic at p0). For the monodromy theorem then implies the existence of a meromorphic function on the surface whose real part is u. Such a meromorphic function has a simple pole at p0 and elsewhere is analytic. It defines a univalent conformal map of the surface onto the extended plane.

scholarly journals On the Tumura-Clunie Theorem and Its Application

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Gaixian Xue ◽  
Jinjin Huang
Keyword(s):  
Meromorphic Functions ◽  
Simple Pole

We cast aside the restriction of the simple pole in the Tumura-Clunie type theorems for meromorphic functions and obtain a better result which improves the earlier results of Y. D. Ren. Furthermore, as an application, we improve a theorem given by B. Y. Su.

scholarly journals Two numerical methods for Abel's integral equation with comparison

2012 ◽  
Vol Volume 15, 2012 ◽  
Author(s):  
Abdallah Ali Badr
Keyword(s):  
Integral Equation ◽  
Numerical Methods ◽  
Fractional Order ◽  
Quadrature Formula ◽  
Approximate Formula ◽  
Simple Pole ◽  
Numerical Examples ◽  
International Audience ◽  
Modified Formula

International audience Analogy between Abel's integral equation and the integral of fractional order of a given function, j^α f(t), is discussed. Two different numerical methods are presented and an approximate formula for j^α f(t) is obtained. The first approach considers the case when the function, f(t), is smooth and a quadrature formula is obtained. A modified formula is deduced in case the function has one or more simple pole. In the second approach, a procedure is presented to weaken the singularities. Both two approaches could be used to solve numerically Abel's integral equation. Some numerical examples are given to illustrate our results.

scholarly journals Modified L-functions

2008 ◽  
Vol 48 ◽  
Author(s):  
Eugenijus Stankus
Keyword(s):  
Zeta Function ◽  
Prime Numbers ◽  
Simple Pole

The sequence of generalized prime numbers q0 = 1, qn = pkn+1 -1, n ∈ N, and the corresponding zeta-function Zk(s) = \prodp>2( 1 - (pk - 1)-s)-1 , s = σ + it, are analyzed. The analyticity of Zk(s) in the domain σ > 0, except for a simple pole s = 1/k , is proved.

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