On one generalized integral transform of the Bessel type

Authors

  • N. O. Virchenko
  • M. O. Chetvertak

DOI:

https://doi.org/10.15407/dopovidi2014.12.024

Keywords:

basic properties, generalization of the Bessel function, integral representation

Abstract

A generalization of the Bessel function is introduced. Its integral representation and basic properties are given. A generalized integral transform of the Bessel type is constructed. The inversion formula of this integral transform is given.

Downloads

Download data is not yet available.

References

Kilbas A. A., Saigo M. H-transforms. London: Chapman and Hall, 2004. https://doi.org/10.1201/9780203487372

Virchenko N. O. Generalized integral transformation, Kyiv: Zadruga, 2013 (in Ukrainian).

Akhiezer N. I. Lectures on integral transforms, Kharkov: Vuscha shk., 1984 (in Russian).

Bruchkov Yu. A., Prudnikov A. P., Shushov V. S. Operational calculus In: The results of science and technology. Mathematical analysis, Moscow: VINITI AN USSR, 1979: 99–148 (in Russian).

Samoilenko A. M., Krivosheia S. A., Perestiyk M. O. Differential equations in problems, Kyiv: Lubid, 2003 (in Ukrainian).

Beitmen G., Erdeii A. Higher transcendental functions. Vol. 1, Moscow: Nauka, 1965 (in Russian).

Vatson G. N. The theory of Bessel functions. Pt. 1, Moscow: Izd-vo inostr. lit., 1949 (in Russian).

Downloads

Published

19.03.2025

How to Cite

Virchenko, N. O., & Chetvertak, M. O. (2025). On one generalized integral transform of the Bessel type . Reports of the National Academy of Sciences of Ukraine, (6), 24–28. https://doi.org/10.15407/dopovidi2014.12.024

Issue

No. 6 (2022): Reports of the National Academy of Sciences of Ukraine

Section

Mathematics

License

Copyright (c) 2025 Reports of the National Academy of Sciences of Ukraine

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.