THE MELLIN INTEGRAL TRANSFORM AND ITS APPLICATIONS

Authors

Teshayeva Gulhayo Farhod kizi

Keywords:

Mellin integral transform; integral transforms; asymptotic analysis; special functions; scale invariance; mathematical analysis; applied mathematics

Abstract

This article is devoted to the study of the Mellin integral transform and its applications in modern mathematical analysis. The paper examines the theoretical foundations of the Mellin transform, its fundamental properties, and its relationship with other classical integral transforms. Particular attention is paid to the role of the Mellin transform in solving problems involving scale invariance, asymptotic behavior, and multiplicative convolution. The study demonstrates that the Mellin transform provides an efficient analytical framework for evaluating improper integrals, analyzing special functions, and simplifying complex mathematical expressions. In addition, the article highlights practical applications of the Mellin transform in mathematical physics, signal and image processing, algorithm analysis, and other applied fields. The results confirm that the Mellin integral transform is a versatile and powerful tool that bridges theoretical and applied mathematics, offering broad potential for further research and development.

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References

Bracewell, R. N. (2000). The Fourier Transform and Its Applications. 3rd ed. New York: McGraw-Hill.

Debnath, L., & Bhatta, D. (2015). Integral Transforms and Their Applications. 3rd ed. Boca Raton: CRC Press.

Flajolet, P., Gourdon, X., & Dumas, P. (1995). Mellin transforms and asymptotics: Harmonic sums. Theoretical Computer Science, 144(1–2), 3–58.

Paris, R. B., & Kaminski, D. (2001). Asymptotics and Mellin–Barnes Integrals. Cambridge: Cambridge University Press.

Titchmarsh, E. C. (1986). Introduction to the Theory of Fourier Integrals. 2nd ed. Oxford: Oxford University Press.

Yakubovich, S., & Luchko, Y. (1994). The Hypergeometric Approach to Integral Transforms and Convolutions. Dordrecht: Kluwer Academic Publishers.

Butzer, P. L., Jansche, S., & Stens, R. L. (2000). Mellin transform theory and the Paley–Wiener theorem. Integral Transforms and Special Functions, 11(4), 325–341.

Andrews, G. E., Askey, R., & Roy, R. (1999). Special Functions. Cambridge: Cambridge University Press.

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Published

2026-02-06

How to Cite

Teshayeva Gulhayo Farhod kizi. (2026). THE MELLIN INTEGRAL TRANSFORM AND ITS APPLICATIONS. International Multidisciplinary Journal for Research & Development, 13(02). Retrieved from https://www.ijmrd.in/index.php/imjrd/article/view/5010