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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2014, Issue 4(37), Pages 16–21 (Mi vsgtu1361)  

Differential Equations

On one generalization of Bessel function

N. A. Virchenko, M. A. Chetvertak

National Technical University of Ukraine "Kiev Polytechnic Institute", Kiev, 03056, Ukraine

Abstract: In this paper the generalized Bessel function $J_{\mu ,\omega } ( x )$ is introduced. The function $J_{\mu ,\omega } ( x )$ is given as one solution of the following differential equation:
$$ x^2{y}"+x{y}'+( {x-\mu ^2} )( {x+\omega ^2} )y=0, \quad \mu , \omega \notin \mathbb Z. $$
The representation of the $J_{\mu ,\omega } ( x )$ by the power series is given. The theorem on integral representations of the function $J_{\mu ,\omega } ( x )$ is established. The main properties of the function $J_{\mu ,\omega } ( x )$ are studied. The integral transforms of Bessel type with the function $J_{\mu ,\omega } ( x )$ is constructed. Formula of inversion of this transform is received.

Keywords: Bessel function, hypergeometric function, integral transform
Author to whom correspondence should be addressed

DOI: https://doi.org/10.14498/vsgtu1361

Full text: PDF file (707 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 517.584, 517.923
MSC: 33C10, 34B30
Original article submitted 03/XI/2014
revision submitted – 26/XI/2014

Citation: N. A. Virchenko, M. A. Chetvertak, “On one generalization of Bessel function”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 4(37) (2014), 16–21

Citation in format AMSBIB
\Bibitem{VirChe14}
\by N.~A.~Virchenko, M.~A.~Chetvertak
\paper On one generalization of Bessel function
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2014
\vol 4(37)
\pages 16--21
\mathnet{http://mi.mathnet.ru/vsgtu1361}
\crossref{https://doi.org/10.14498/vsgtu1361}
\zmath{https://zbmath.org/?q=an:06968929}
\elib{https://elibrary.ru/item.asp?id=23464548}


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  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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