Application of Anuj Transform for Solving Improper Integrals whose Kernels Contain Bessel Functions of First Kind
Keywords:
Integral Transform, Improper Integrals, Bessel Function, Anuj TransformAbstract
Improper integrals play a crucial role in both pure and applied mathematics, especially in problems involving unbounded functions or infinite intervals. These integrals arise naturally in the solutions of the problems of gravitational fields, heat conduction, electromagnetic theory, and probability distributions. However, determining the value of improper integrals is often challenging task due to the presence of infinite limits or singularities within the interval of integration. Motivated by these challenges, this study focuses on the development and application of the Anuj transform as an effective tool for handling improper integrals whose kernels contain Bessel functions of the first kind. The Anuj transform is employed to reformulate complex integrals into more tractable forms, thereby facilitating their analytical evaluation. By applying this approach, the study demonstrates a significant reduction in computational burden, alongside acceleration in the overall process of integral evaluation. The findings presented in this paper indicate that the Anuj transform has not only significantly accelerated the overall process of evaluation of improper integrals but has also substantially reduced the associated computational burden. This reduction in computational load reinforces the potential of the Anuj transform for practical uses within engineering applications and other related fields, showcasing its promise as a powerful tool in mathematical analysis and applied science. Future investigations may explore its integration with numerical schemes and its adaptability to other classes of special functions.
How to cite this article:
Aggarwal S. Application of Anuj Transform for Solving Improper Integrals whose Kernels Contain Bessel Functions of First Kind. J Adv Res Appl Math Stat, Vol 11, Issue 3&4 2026: Pg. No. 47-54.
DOI: https://doi.org/10.24321/2455.7021.202609
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