A Versatile Integral in Physics and Astronomy and Fox’s H-Function

A real scalar variable integral is known in the literature by different names in different disciplines. It is basically a Bessel integral called specifically Krätzel integral. An integral transform with this Krätzel function as kernel is known as Krätzel transform. This article examines some mathematical properties of Krätzel integral, its connection to Mellin convolutions and statistical distributions, its computable representations, and its extensions to multivariate and matrix-variate cases, in both the real and complex domains. An extension in the pathway family of functions is also explored.

show abstract

“…See also the versatile integral discussed in [15]. Various types of extensions of Krätzel integrals are involved in Equation (28).…”

Section: Pathway Extension Of Krätzel Integralmentioning

confidence: 99%

Mathematical Aspects of Krätzel Integral and Krätzel Transform

Mathai

Haubold

2020

Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

New Results Involving the Generalized Krätzel Function with Application to the Fractional Kinetic Equations

Tassaddiq

Srivastava

2023

Mathematics

View full text Add to dashboard Cite

Sun is a basic component of the natural environment and kinetic equations are important mathematical models to assess the rate of change of chemical composition of a star such as the sun. In this article, a new fractional kinetic equation is formulated and solved using generalized Krätzel integrals because the nuclear reaction rate in astrophysics is represented in terms of these integrals. Furthermore, new identities involving Fox–Wright function are discussed and used to simplify the results. We compute new fractional calculus formulae involving the Krätzel function by using Kiryakova’s fractional integral and derivative operators which led to several new identities for a variety of other classic fractional transforms. A number of new identities for the generalized Krätzel function are then analyzed in relation to the H- function. The closed form of such results is also expressible in terms of Mittag-Leffler function. Distributional representation of Krätzel function and its Laplace transform has been essential in achieving the goals of this work.

show abstract

A New Representation of the Generalized Krätzel Function

Tassaddiq¹

2020

Mathematics

View full text Add to dashboard Cite

The confluence of distributions (generalized functions) with integral transforms has become a remarkably powerful tool to address important unsolved problems. The purpose of the present study is to investigate a distributional representation of the generalized Krätzel function. Hence, a new definition of these functions is formulated over a particular set of test functions. This is validated using the classical Fourier transform. The results lead to a novel extension of Krätzel functions by introducing distributions in terms of the delta function. A new version of the generalized Krätzel integral transform emerges as a natural consequence of this research. The relationship between the Krätzel function and the H-function is also explored to study new identities.

show abstract

A Versatile Integral in Physics and Astronomy and Fox’s H-Function

Cited by 3 publications

References 14 publications

Mathematical Aspects of Krätzel Integral and Krätzel Transform

Mathematical Aspects of Krätzel Integral and Krätzel Transform

New Results Involving the Generalized Krätzel Function with Application to the Fractional Kinetic Equations

A New Representation of the Generalized Krätzel Function

Contact Info

Product

Resources

About