Optical implementation of integral transforms with Bessel function kernels

1982 ◽  
Vol 7 (3) ◽  
pp. 124
Author(s):  
R. A. Athale ◽  
H. H. Szu ◽  
J. N. Lee
Keyword(s):  
Bessel Function ◽  
Integral Transforms

scholarly journals Integral transforms of an extended generalized multi-index Bessel function

2020 ◽  
Vol 5 (6) ◽  
pp. 7531-7546 ◽  
Author(s):  
Shahid Mubeen ◽  
◽  
Rana Safdar Ali ◽  
Iqra Nayab ◽  
Gauhar Rahman ◽  
...  
Keyword(s):  
Bessel Function ◽  
Integral Transforms ◽  
Multi Index

scholarly journals Generalized Fractional Integral Formulas for the k-Bessel Function

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
D. L. Suthar ◽  
Mengesha Ayene
Keyword(s):  
Bessel Function ◽  
Hypergeometric Series ◽  
Fractional Integral ◽  
Integral Transforms ◽  
Fractional Integrals ◽  
Liouville Type ◽  
Generalized Hypergeometric Series ◽  
Integral Formulas ◽  
Generalized Fractional Integral ◽  
Appell Function

The aim of this paper is to deal with two integral transforms involving the Appell function as their kernels. We prove some compositions formulas for generalized fractional integrals with k-Bessel function. The results are expressed in terms of generalized Wright type hypergeometric function and generalized hypergeometric series. Also, the authors presented some related assertion for Saigo, Riemann-Liouville type, and Erdélyi-Kober type fractional integral transforms.

Some self-reciprocal functions and kernels

1961 ◽  
Vol 57 (3) ◽  
pp. 690-692 ◽  
Author(s):  
V. Lakshmikanth
Keyword(s):  
Integral Equation ◽  
Bessel Function ◽  
Integral Transforms ◽  
Homogeneous Integral Equation ◽  
Image Position ◽  
Class Of Functions

The aim of this note is to find out some self-reciprocal functions and kernels for Fourier-Bessel integral transforms. Following Hardy and Titchmarsh(i), we shall denote by Rp the class of functions which satisfy the homogeneous integral equationwhere Jp(x) is a Bessel function of order p ≥ − ½. For particular values of p = ½, − ½, we write Rs and Rc irrespectively.

Fractional Integration of Generalized Bessel Function of the First Kind

2011 ◽  
Author(s):  
Pradeep Malik ◽  
Saiful R. Mondal ◽  
A. Swaminathan
Keyword(s):  
Bessel Function ◽  
Hypergeometric Functions ◽  
Fractional Integration ◽  
Integral Transforms ◽  
Generalized Hypergeometric Functions ◽  
Fractional Integral Operators ◽  
Generalized Bessel Function ◽  
Hyperbolic Sine ◽  
Hyperbolic Cosine ◽  
Special Cases

Generalizing the classical Riemann-Liouville and Erde´yi-Kober fractional integral operators two integral transforms involving Gaussian hypergeometric functions in the kernel are considered. Formulas for composition of such integrals with generalized Bessel function of the first kind are obtained. Special cases involving trigonometric functions such as sine, cosine, hyperbolic sine and hyperbolic cosine are deduced. These results are established in terms of generalized Wright function and generalized hypergeometric functions.

On Self-reciprocal functions for Fourier-Bessel integral transforms

1961 ◽  
Vol 57 (4) ◽  
pp. 778-781
Author(s):  
Afzal Ahmad ◽  
V. Lakshmikanth
Keyword(s):  
Bessel Function ◽  
Integral Transform ◽  
Integral Transforms ◽  
Special Cases ◽  
Image Position

Following Hardy and Titchmarsh(1) a function f(x) is said to be self-reciprocal if it satisfies the Fourier-Bessel integral transformwhere Jp(x) is a Bessel function of order P ≥ –½. This integral is denoted by Rp. The special cases P ½ and P ½, we denote by Rs and Rc, respectively.

scholarly journals An integral transform and its application in the propagation of Lorentz-Gaussian beams

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
A. Belafhal ◽  
E.M. El Halba ◽  
T. Usman
Keyword(s):  
Bessel Function ◽  
Optical System ◽  
Present Note ◽  
Integral Transform ◽  
Integral Transforms ◽  
Whittaker Function ◽  
Higher Order ◽  
Gaussian Beams ◽  
Special Values ◽  
Abcd Optical System

Abstract The aim of the present note is to derive an integral transform I = ∫ 0 ∞ x s + 1 e - β x 2 + γ x M k , v ( 2 ζ x 2 ) J μ ( χ x ) d x , I = \int_0^\infty {{x^{s + 1}}{e^{ - \beta x}}^{2 + \gamma x}{M_{k,v}}} \left( {2\zeta {x^2}} \right)J\mu \left( {\chi x} \right)dx, involving the product of the Whittaker function Mk, ν and the Bessel function of the first kind Jµ of order µ. As a by-product, we also derive certain new integral transforms as particular cases for some special values of the parameters k and ν of the Whittaker function. Eventually, we show the application of the integral in the propagation of hollow higher-order circular Lorentz-cosh-Gaussian beams through an ABCD optical system (see, for details [13], [3]).

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