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

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 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.

scholarly journals Fractional calculus of a product of multivariable Srivastava polynomial and multi-index Bessel function in the kernel F3

2020 ◽  
Vol 5 (2) ◽  
pp. 1462-1475 ◽  
Author(s):  
Owais Khan ◽  
◽  
Nabiullah Khan ◽  
Kottakkaran Sooppy Nisar ◽  
Mohd. Saif ◽  
...  
Keyword(s):  
Fractional Calculus ◽  
Bessel Function ◽  
Multi Index

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.

scholarly journals Estimation of certain integrals with extended multi-index Bessel function

2019 ◽  
Vol 7 (2) ◽  
pp. 206-212 ◽  
Author(s):  
M. Kamarujjama ◽  
N.U. Khan ◽  
Owais Khan
Keyword(s):  
Bessel Function ◽  
Multi Index

scholarly journals Multi-Dimensional Chebyshev Polynomials: A Non-Conventional Approach

2019 ◽  
Vol 10 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Clemente Cesarano
Keyword(s):  
Chebyshev Polynomials ◽  
Polynomial Interpolation ◽  
Hermite Polynomials ◽  
Integral Transforms ◽  
Multi Index ◽  
Special Cases ◽  
The Laplace Transform ◽  
Translation Operators ◽  
Sturm Liouville ◽  
Symbolic Approach

Abstract Chebyshev polynomials are traditionally applied to the approximation theory where are used in polynomial interpolation and also in the study of di erential equations, in particular in some special cases of Sturm-Liouville di erential equation. Many of the operational techniques presented, by using suitable integral transforms, via a symbolic approach to the Laplace transform, allow us to introduce polynomials recognized belonging to the families of Chebyshev of multi-dimensional type. The non-standard approach come out from the theory of multi-index Hermite polynomials, in particular by using the concepts and the related formalism of translation operators.

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
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