scholarly journals K-Bessel functions associated to a 3-rank Jordan algebra

2005 ◽  
Vol 2005 (18) ◽  
pp. 2863-2870
Author(s):  
Hacen Dib
Keyword(s):  
Bessel Function ◽  
Linear Combination ◽  
Jordan Algebra ◽  
Bessel Functions

Using the Bessel-Muirhead system, we can express theK-Bessel function defined on a Jordan algebra as a linear combination of the J-solutions. We determine explicitly the coefficients when the rank of this Jordan algebra is three after a reduction to the rank two. The main tools are some algebraic identities developed for this occasion.

scholarly journals K-Bessel functions in two variables

2003 ◽  
Vol 2003 (14) ◽  
pp. 909-916
Author(s):  
Hacen Dib
Keyword(s):  
Bessel Function ◽  
Linear Combination ◽  
Explicit Formula ◽  
Bessel Functions ◽  
Higher Rank

The Bessel-Muirhead hypergeometric system (or0F1-system) in two variables (and three variables) is solved using symmetric series, with an explicit formula for coefficients, in order to express theK-Bessel function as a linear combination of the J-solutions. Limits of this method and suggestions for generalizations to a higher rank are discussed.

Higher monotonicity properties of normalized Bessel functions

2014 ◽  
Vol 12 (05) ◽  
pp. 1461007
Author(s):  
Yongping Liu
Keyword(s):  
Bessel Function ◽  
Bessel Functions ◽  
Positive Zero ◽  
Local Maxima ◽  
Monotonicity Properties

Denote by Jν the Bessel function of the first kind of order ν and μν,k is its kth positive zero. For ν > ½, a theorem of Lorch, Muldoon and Szegö states that the sequence [Formula: see text] is decreasing, another theorem of theirs states that the sequence [Formula: see text] has higher monotonicity properties. In the present paper, we proved that when ν > ½ the sequence [Formula: see text] has higher monotonicity properties and the properties imply those of the sequence of the local maxima of the function x-ν+1|Jν-1(x)|, x ∈ (0, ∞), i.e. the sequence [Formula: see text] has higher monotonicity properties.

On the Points of Inflection of Bessel Functions of Positive Order, I

1990 ◽  
Vol 42 (5) ◽  
pp. 933-948 ◽  
Author(s):  
Lee Lorch ◽  
Peter Szego
Keyword(s):  
Bessel Function ◽  
Bessel Functions ◽  
Primary Concern ◽  
Second Derivative ◽  
Positive Order ◽  
Fixed Rank

The primary concern addressed here is the variation with respect to the order v > 0 of the zeros jʺvk of fixed rank of the second derivative of the Bessel function Jv(x) of the first kind. It is shown that jʺv1 increases 0 < v < ∞ (Theorem 4.1) and that jʺvk increases in 0 < v ≤ 3838 for fixed k = 2, 3,… (Theorem 10.1).

scholarly journals The zeros of bessel functions.

1918 ◽  
Vol 94 (659) ◽  
pp. 190-206 ◽  
Keyword(s):  
Bessel Function ◽  
Bessel Functions ◽  
Practical Importance ◽  
Zeros Of Bessel Functions ◽  
Order Of Magnitude ◽  
Low Order

1. Although many results are known concerning the zeros of Bessel functions,* the greater number of these results are of practical importance only in the case of functions of comparatively low order. For example, McMahon has given a formula† for calculating the zeros of the Bessel function J n ( x ), namely that, if k 1 , k 2 , k 3 , ..., are the positive zeros arranged in ascending order of magnitude, then ks = β- 4 n 2 -1/8β - 4(4 n 2 -1)(28 n 2 -31)/3.(8β) 3 -..., where β = 1/4 π (2 n +4 s —1).

scholarly journals Unified integrals involving product of multivariable polynomials and generalized Bessel functions

2019 ◽  
Vol 38 (6) ◽  
pp. 73-83
Author(s):  
K. S. Nisar ◽  
D. L. Suthar ◽  
Sunil Dutt Purohit ◽  
Hafte Amsalu
Keyword(s):  
Bessel Function ◽  
Bessel Functions ◽  
General Character ◽  
Polynomial Functions ◽  
Finite Product ◽  
Generalized Bessel Function ◽  
Integral Formulas ◽  
Generalized Bessel Functions ◽  
Multivariable Polynomial ◽  
Integral Formulae

The aim of this paper is to evaluate two integral formulas involving a finite product of the generalized Bessel function of the first kind and multivariable polynomial functions which results are expressed in terms of the generalized Lauricella functions. The major results presented here are of general character and easily reducible to unique and well-known integral formulae.

A family of hyper-Bessel functions and convergent series in them

2014 ◽  
Vol 17 (4) ◽  
Author(s):  
Jordanka Paneva-Konovska
Keyword(s):  
Power Series ◽  
Bessel Function ◽  
Classical Theory ◽  
Bessel Functions ◽  
Differential Operators ◽  
Arbitrary Order ◽  
Convergent Series ◽  
Multi Index ◽  
Fatou Theorem ◽  
Convergence Of Series

AbstractThe Delerue hyper-Bessel functions that appeared as a multi-index generalizations of the Bessel function of the first type, are closely related to the hyper-Bessel differential operators of arbitrary order, introduced by Dimovski. In this work we consider an enumerable family of hyper-Bessel functions and study the convergence of series in such a kind of functions. The obtained results are analogues to the ones in the classical theory of the widely used power series, like Cauchy-Hadamard, Abel and Fatou theorem.

scholarly journals Certain Fractional Integral Formulas Involving the Product of Generalized Bessel Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
D. Baleanu ◽  
P. Agarwal ◽  
S. D. Purohit
Keyword(s):  
Bessel Function ◽  
Fractional Integral ◽  
Bessel Functions ◽  
Fractional Integration ◽  
Fractional Integrals ◽  
General Character ◽  
Generalized Bessel Function ◽  
Integral Formulas ◽  
Generalized Bessel Functions ◽  
Special Cases

We apply generalized operators of fractional integration involving Appell’s functionF3(·)due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.

On a new formula for the transient state probabilities for M/M/1 queues and computational implications

1993 ◽  
Vol 30 (1) ◽  
pp. 237-246 ◽  
Author(s):  
B. W. Conolly ◽  
Christos Langaris
Keyword(s):  
Bessel Function ◽  
Bessel Functions ◽  
Queueing Systems ◽  
Computation Time ◽  
Transient State ◽  
Time Dependent ◽  
Traffic Intensity ◽  
New Formula ◽  
State Component ◽  
Dependent State

Past work relating to the computation of time-dependent state probabilities in M/M/1 queueing systems is reviewed, with emphasis on methods that avoid Bessel functions. A new series formula of Sharma [13] is discussed and its connection with traditional Bessel function series is established. An alternative new series is developed which isolates the steady-state component for all values of traffic intensity and which turns out to be computationally superior. A brief comparison of our formula, Sharma's formula, and a classical Bessel function formula is given for the computation time of the probability that an initially empty system is empty at time t later.

Some orthogonal and complete sets of Bessel functions associated with the vibrating plate

1982 ◽  
Vol 91 (3) ◽  
pp. 503-515 ◽  
Author(s):  
J. R. Higgins
Keyword(s):  
Bessel Function ◽  
Bessel Functions ◽  
Main Concern ◽  
Edge Type ◽  
Completeness Criterion ◽  
Complete Sets ◽  
Clamped Edge ◽  
Vibrating Plate

AbstarctSome orthogonal sets of Bessel functions of real order v are identified using the equation Δ2u = utt of the vibrating plate. Our main concern is with the L2 completeness of such sets, and we prove that the well known ‘clamped edge’ type is complete for v > -1, thus completing a result of E. Dahlberg. We also study a very closely related set and show that it needs an extra (non-Bessel) function for completeness.Our method for proving the completeness is based on one given by H. Hochstadt in connection with Dini functions. We have found it necessary to reorganize Hoch-stadt's method and correct some errors contained in it.Certain isolated values of v require special attention and we treat these by subjecting the Dalzell completeness criterion to a continuity argument.

scholarly journals Application of the Bessel function to compute the air pollutant with the stratification of the atmospheric

2015 ◽  
Vol 18 (2) ◽  
pp. 14-20
Author(s):  
Dung Anh Tran ◽  
Hang Thi Chu ◽  
Long Ta Bui
Keyword(s):  
Differential Equation ◽  
Bessel Function ◽  
Bessel Functions ◽  
Analytic Solutions ◽  
Air Pollutant ◽  
Spherical Coordinates ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Bessel Differential Equation ◽  
Separation Of Variable

The Bessel differential equation with the Bessel function of solution has been applied. Bessel functions are the canonical solutions of Bessel's differential equation. Bessel's equation arises when finding separable solutions to Laplace's equation in cylindrical or spherical coordinates. Bessel functions are important for many problems of advection–diffusion progress and wave propagation. In this paper, authors present the analytic solutions of the atmospheric advection-diffusion equation with the stratification of the boundary condition. The solution has been found by applied the separation of variable method and Bessel’s equation.

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