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.

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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).

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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, (12), 24–28. https://doi.org/10.15407/dopovidi2014.12.024

Issue

No. 12 (2014): Reports of the National Academy of Sciences of Ukraine

Section

Mathematics

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

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