ASYMPTOTICS OF ZEROS OF CERTAIN ENTIRE FUNCTIONS

2007 ◽  
Vol 05 (03) ◽  
pp. 291-299
Author(s):  
MOURAD E. H. ISMAIL
Keyword(s):  
Closed Form ◽  
Bessel Functions ◽  
Entire Functions

We derive representations for some entire q-functions and use it to derive asymptotics and closed form expressions for large zeros of a class of entire functions including the Ramanujan function, and q-Bessel functions.

scholarly journals A Review of Procedures for Summing Kapteyn Series in Mathematical Physics

2009 ◽  
Vol 2009 ◽  
pp. 1-34 ◽  
Author(s):  
R. C. Tautz ◽  
I. Lerche
Keyword(s):  
Closed Form ◽  
Bessel Functions ◽  
Mathematical Physics ◽  
Short Review ◽  
Quantum Systems ◽  
Review Article ◽  
Functional Behavior ◽  
Basic Physics ◽  
Kapteyn Series ◽  
Physics Problems

Since the discussion of Kapteyn series occurrences in astronomical problems the wealth of mathematical physics problems in which such series play dominant roles has burgeoned massively. One of the major concerns is the ability to sum such series in closed form so that one can better understand the structural and functional behavior of the basic physics problems. The purpose of this review article is to present some of the recent methods for providing such series in closed form with applications to: (i) the summation of Kapteyn series for radiation from pulsars; (ii) the summation of other Kapteyn series in radiation problems; (iii) Kapteyn series arising in terahertz sideband spectra of quantum systems modulated by an alternating electromagnetic field; and (iv) some plasma problems involving sums of Bessel functions and their closed form summation using variations of the techniques developed for Kapteyn series. In addition, a short review is given of some other Kapteyn series to illustrate the ongoing deep interest and involvement of scientists in such problems and to provide further techniques for attempting to sum divers Kapteyn series.

MODELING NON-LINEAR COHERENT STATES IN FIBER ARRAYS

2011 ◽  
Vol 09 (supp01) ◽  
pp. 349-355 ◽  
Author(s):  
R. DE J. LEÓN-MONTIEL ◽  
H. MOYA-CESSA
Keyword(s):  
Closed Form ◽  
Coherent States ◽  
Bessel Functions ◽  
Displacement Operator ◽  
Fiber Arrays ◽  
Non Linear ◽  
Phase Operators

A class of nonlinear coherent states related to the Susskind-Glogower (phase) operators is obtained. We call these nonlinear coherent states as Bessel states because the coefficients that expand them into number states are Bessel functions. We give a closed form for the displacement operator that produces such states.

Summation of Series over Bourget Functions

2008 ◽  
Vol 51 (4) ◽  
pp. 627-636
Author(s):  
Mirjana V. Vidanović ◽  
Slobodan B. Tričković ◽  
Miomir S. Stanković
Keyword(s):  
Closed Form ◽  
Infinite Series ◽  
Bessel Functions ◽  
Integer Order ◽  
Summation Of Series ◽  
Finite Sums ◽  
Riemann Ζ Function

AbstractIn this paper we derive formulas for summation of series involving J. Bourget's generalization of Bessel functions of integer order, as well as the analogous generalizations by H. M. Srivastava. These series are expressed in terms of the Riemann ζ function and Dirichlet functions η, λ, β, and can be brought into closed form in certain cases, which means that the infinite series are represented by finite sums.

scholarly journals An Approximate Analysis and Its Application to The Non-Linear Performance of Three Mosfet Transconductance Amplifiers

1994 ◽  
Vol 17 (3) ◽  
pp. 135-149
Author(s):  
Muhammad Taher Abuelma'atti
Keyword(s):  
Closed Form ◽  
Bessel Functions ◽  
Electronic Circuit ◽  
Simple Procedure ◽  
Approximate Analysis ◽  
Electronic Circuits ◽  
Input Output ◽  
Non Linear ◽  
Transconductance Amplifiers ◽  
Analytical Expressions

A simple procedure for approximating the input-output characteristic of non-linear electronic circuits is presented. Using this procedure, closed-form analytical expressions, in terms of the ordinary Bessel functions, are obtained for the output spectra of a non-linear electronic circuit resulting from a multisinusoidal input. Using these expressions, the non-linear performance of three basic MOSFET transconductance amplifiers is considered in an attempt to determine the transistor parameters for best linearity.

scholarly journals ETHOD OF COMPENSATING LOADS FOR SOLVING OF ANISOTROPIC MEDIUM PROBLEMS

2018 ◽  
Vol 14 (1) ◽  
pp. 71-77
Author(s):  
Elena B. Koreneva
Keyword(s):  
Closed Form ◽  
Anisotropic Medium ◽  
Bessel Functions ◽  
Circular Plates ◽  
Cylindrical Anisotropy

The work applies the method of compensating loads (MCL) for solution of statics and vibrations problems of plates with cylindrical anisotropy. For receiving of basic and compensating solutions Nielsen’s equation is used. The solution expressed in terms of Bessel functions is obtained. Such way can be used in con-sideration of symmetric, antisymmetric and unsymmetric flexure of orthotropic circular plates resting on an elastic Winkler’s subgrade. The similar method can be also utilized for examination of the symmetric vibrations of the orthotropic circular plates as well as for the cases of vibrations with one or a few nodal diameters. The solutions are obtained in closed form in terms of the cylindrical functions.

scholarly journals METHOD OF COMPENSATING LOADS FOR SOLVING OF A PROBLEM OF UNSYMMETRIC BENDING OF INFINITE ICE SLAB WITH CIRCULAR OPENING

2017 ◽  
Vol 13 (2) ◽  
pp. 50-55
Author(s):  
Elena B. Koreneva
Keyword(s):  
Closed Form ◽  
Bessel Functions ◽  
Infinite Plate ◽  
Constant Thickness ◽  
Circular Opening ◽  
Opening Method

Unsymmetric flexure of an infinite ice slab with circular opening is under examination. The men-tioned construction is considered as an infinite plate of constant thickness resting on an elastic subgrade which properties are described by Winkler’s model. The plate’s thickness is variable in the area ajoining to the opening. Method of compensating loads is used. Basic and compensating solutions are received. The obtained solutions are produced in closed form in terms of Bessel functions.

scholarly journals Representation formulas for entire functions of exponential type and generalized bernoulli polynomials

1998 ◽  
Vol 64 (3) ◽  
pp. 307-316 ◽  
Author(s):  
C. Frappier
Keyword(s):  
Entire Function ◽  
Exponential Type ◽  
General Class ◽  
Bessel Functions ◽  
Entire Functions ◽  
Bernoulli Polynomials ◽  
Representation Formulas ◽  
Functions Of Exponential Type ◽  
Generalized Bernoulli Polynomials

AbstractWe introduce a sequence of polynomials which are extensions of the classic Bernoulli polynomials. This generalization is obtained by using the Bessel functions of the first kind. We use these polynomials to evaluate explicitly a general class of series containing an entire function of exponential type.

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