scholarly journals On improper integrals of products of logarithmic, power and Bessel functions

1992 ◽  
Vol 45 (3) ◽  
pp. 395-398
Author(s):  
M. Aslam Chaudhry ◽  
M. Ahmad
Keyword(s):  
Integral Representation ◽  
Open Problem ◽  
Bessel Functions ◽  
Euler Constant ◽  
Special Cases ◽  
Improper Integrals

In this paper we have evaluated the integral . A new integral representation of the Euler constant is shown. Some special cases of the result are discussed and an open problem is posed.

Quadruple Integral Involving the Logarithm and Product of Bessel Functions Expressed in Terms of the Lerch Function

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 324
Author(s):  
Robert Reynolds ◽  
Allan Stauffer
Keyword(s):  
Integral Representation ◽  
Bessel Functions ◽  
Fundamental Constants ◽  
Special Cases

In this paper, we have derived and evaluated a quadruple integral whose kernel involves the logarithm and product of Bessel functions of the first kind. A new quadruple integral representation of Catalan’s G and Apéry’s ζ(3) constants are produced. Some special cases of the result in terms of fundamental constants are evaluated. All the results in this work are new.

Asymptotic expansions and converging factors V. Lommel, Struve, modified Struve, Anger and Weber functions, and integrals of ordinary and modified Bessel functions

1959 ◽  
Vol 249 (1257) ◽  
pp. 284-292 ◽  
Keyword(s):  
Asymptotic Expansions ◽  
Bessel Functions ◽  
Modified Bessel Functions ◽  
Lommel Functions ◽  
Special Cases

A theory of Lommel functions is developed, based upon the methods described in the first four papers (I to IV) of this series for replacing the divergent parts of asymptotic expansions by easily calculable series involving one or other of the four ‘basic converging factors’ which were investigated and tabulated in I. This theory is then illustrated by application to the special cases of Struve, modified Struve, Anger and Weber functions, and integrals of ordinary and modified Bessel functions.

Transient Analysis of a Two-Heterogeneous Severs Queue with Impatient Behaviour and Multiple Vacations

2018 ◽  
Vol 6 (1) ◽  
pp. 69-84
Author(s):  
Jia Xu ◽  
Liwei Liu ◽  
Taozeng Zhu
Keyword(s):  
Generating Functions ◽  
Transient Analysis ◽  
Bessel Functions ◽  
Queueing System ◽  
System Size ◽  
Heterogeneous Servers ◽  
Modified Bessel Functions ◽  
Multiple Vacations ◽  
Special Cases ◽  
Mean And Variance

AbstractWe consider anM/M/2 queueing system with two-heterogeneous servers and multiple vacations. Customers arrive according to a Poisson process. However, customers become impatient when the system is on vacation. We obtain explicit expressions for the time dependent probabilities, mean and variance of the system size at timetby employing probability generating functions, continued fractions and properties of the modified Bessel functions. Finally, two special cases are provided.

scholarly journals A family of Finch and Skea relativistic stars

2017 ◽  
Vol 26 (03) ◽  
pp. 1750014 ◽  
Author(s):  
S. D. Maharaj ◽  
D. Kileba Matondo ◽  
P. Mafa Takisa
Keyword(s):  
Bessel Functions ◽  
Special Functions ◽  
Graphical Analysis ◽  
System Of Differential Equations ◽  
Elementary Functions ◽  
Relativistic Stars ◽  
Spacetime Geometry ◽  
Special Cases ◽  
Barotropic Equation ◽  
Charged Model

Several new families of exact solution to the Einstein–Maxwell system of differential equations are found for anisotropic charged matter. The spacetime geometry is that of Finch and Skea which satisfies all criteria for physical acceptability. The exact solutions can be expressed in terms of elementary functions, Bessel functions and modified Bessel functions. When a parameter is restricted to be an integer then the special functions reduce to simple elementary functions. The uncharged model of Finch and Skea [R. Finch and J. E. F. Skea, Class. Quantum Grav. 6 (1989) 467.] and the charged model of Hansraj and Maharaj [S. Hansraj and S. D. Maharaj, Int. J. Mod. Phys. D 15 (2006) 1311.] are regained as special cases. The solutions found admit a barotropic equation of state. A graphical analysis indicates that the matter and electric quantities are well behaved.

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.

Derivation of Green-type, transitional, and uniform asymptotic expansions from differential equations II. Whittaker functions W k,m for large k , and for large | K 2 – m 2 |

1964 ◽  
Vol 281 (1384) ◽  
pp. 111-129 ◽  
Keyword(s):  
Differential Equations ◽  
Asymptotic Expansions ◽  
Mellin Transform ◽  
Bessel Functions ◽  
Parabolic Cylinder ◽  
Whittaker Functions ◽  
Transform Method ◽  
Special Cases ◽  
Uniform Expansions ◽  
Uniform Asymptotic Expansions

The method for deriving Green-type asymptotic expansions from differential equations, introduced in I and illustrated therein by detailed calculations on modified Bessel functions, is applied to Whittaker functions W k,m , first for large k , and then for large |k 2 —m 2 |. Following the general theory of I, combination of this procedure with the Mellin transform method yields asymptotic expansions valid in transitional regions, and general uniform expansions. Weber parabolic cylinder and Poiseuille functions are examined as important special cases.

scholarly journals Hermite-Hadamard like inequalities for fractional integral operator via convexity and quasi-convexity with their applications

2021 ◽  
Vol 7 (3) ◽  
pp. 3418-3439
Author(s):  
Jamshed Nasir ◽  
◽  
Shahid Qaisar ◽  
Saad Ihsan Butt ◽  
Hassen Aydi ◽  
...  
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Bessel Functions ◽  
Fractional Operator ◽  
Real Numbers ◽  
Hadamard Inequality ◽  
Special Means ◽  
Special Cases ◽  
Derivatives Of ◽  
Quasi Convexity

<abstract><p>Since the supposed Hermite-Hadamard inequality for a convex function was discussed, its expansions, refinements, and variations, which are called Hermite-Hadamard type inequalities, have been widely explored. The main objective of this article is to acquire new Hermite-Hadamard type inequalities employing the Riemann-Liouville fractional operator for functions whose third derivatives of absolute values are convex and quasi-convex in nature. Some special cases of the newly presented results are discussed as well. As applications, several estimates concerning Bessel functions and special means of real numbers are illustrated.</p></abstract>

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