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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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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2011, Issue 2(23), Pages 8–16
DOI: https://doi.org/10.14498/vsgtu913 (Mi vsgtu913) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Differential Equations

Some new generalized integral transformations and their application in differential equations theory

O. A. Repinab, S. M. Zaikinaca

a Dept. of Applied Mathematics and Computer Science, Samara State Technical University, Samara
b Dept. of Mathematical Statistics and Econometrics, Samara State Economic University, Samara
c Dept. of Computer Science and Experimental Mathematics, Volgograd State University, Volgograd
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DOI: https://doi.org/10.14498/vsgtu913
Abstract: We present new integral transforms, generalized the classical Laplace, Stieltjes and Widder integral transforms in the potential theory. The $(\tau,\beta)$-generalized confluent hypergeometric functions are the kernels of these integral transforms. Inverse formulas for new integral transforms are proved. Relations of the Parseval–Goldstein type are established. Some examples of applications of the new integral transforms are given.
Keywords: integral transforms, Parseval–Goldstein type identity, inversion theorems.
Original article submitted 29/XII/2010
revision submitted – 20/IV/2011
Bibliographic databases:
Document Type: Article
UDC: 517.581
MSC: Primary 33C15; Secondary 44A15
Language: Russian
Citation: O. A. Repin, S. M. Zaikina, “Some new generalized integral transformations and their application in differential equations theory”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2(23) (2011), 8–16
Citation in format AMSBIB
\Bibitem{RepZai11}
\by O.~A.~Repin, S.~M.~Zaikina
\paper Some new generalized integral transformations and their application in differential equations theory
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2011
\vol 2(23)
\pages 8--16
\mathnet{http://mi.mathnet.ru/vsgtu913}
\crossref{https://doi.org/10.14498/vsgtu913}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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