TWO-DIMENSIONAL INTEGRAL TRANSFORMATIONS WITH KUMMER FUNCTION AND HYPERGEOMETRIC GAUSSIAN FUNCTION IN KERNELS AS SPECIAL CASES OF TWO-DIMENSIONAL INTEGRAL G-TRANSFORMATION

Article Sidebar

Abstract views: 129
PDF Downloads: 48
pdf (rus) (Русский)
Published: Apr 18, 2023
DOI: https://doi.org/10.52928/2070-1624-2023-40-1-84-91
Keywords:
двумерное интегральное G-преобразование, G-функция Мейера, вырожденная гипергеометрическая функция Куммера, гипергеометрическая функция Гаусса, двумерное преобразование Меллина, пространство интегрируемых функций, дробные интегралы и производные two-dimensional integral G-transformation, Meijer G-function, confluent hypergeometric Kummer function, Gauss hypergeometric function, two-dimensional Mellin transform, space of integrable functions, fractional integrals and derivatives

Main Article Content

S. SITNIK
Belgorod State National Research University "BelGU", Russia
O. SKOROMNIK
Euphrosyne Polotskaya State University of Polotsk
K. VASILEVICH
Euphrosyne Polotskaya State University of Polotsk

Abstract

Two two-dimensional integral transformations with confluent hypergeometric Kummer function and Gauss hypergeometric function in kernels are considered. Applying the Mellin transformation technique, we show that they are special cases of a two-dimensional G-transformation. Based on the theory of the G-transformation, the properties of the considered integral transformations in the weight spaces of integrable functions in the domain  are investigated. The results of the study generalize the results obtained earlier for the corresponding one-dimensional analogues.

Article Details

How to Cite
SITNIK, S., SKOROMNIK, O., & VASILEVICH, K. (2023). TWO-DIMENSIONAL INTEGRAL TRANSFORMATIONS WITH KUMMER FUNCTION AND HYPERGEOMETRIC GAUSSIAN FUNCTION IN KERNELS AS SPECIAL CASES OF TWO-DIMENSIONAL INTEGRAL G-TRANSFORMATION. Vestnik of Polotsk State University. Part C. Fundamental Sciences, (1), 84-91. https://doi.org/10.52928/2070-1624-2023-40-1-84-91
Issue
No. 1 (2023)
Section
mathematics
Creative Commons License

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

Author Biographies

S. SITNIK, Belgorod State National Research University "BelGU", Russia

д-р физ.-мат. наук, доц.

O. SKOROMNIK, Euphrosyne Polotskaya State University of Polotsk

канд. физ.-мат. наук, доц.

Crossref
Scopus
Google Scholar
Europe PMC

References

Papkovich, M. V., & Skoromnik, O. V. (2019). Dvumernoe integral'noe preobrazovanie s G-funktsiei Meiera v yadre v prostranstve summiruemykh funktsii [Two-Dimentional Integral Transform With the Meijer G-Function in the Kernel in the Space of Summable Functions]. Vestnik Polotskogo gosudarstvennogo universiteta. Seriya C, Fundamental'nye nauki [Herald of Polotsk State University. Series С. Fundamental sciences], (4), 131–136. (In Russ., abstr. in Engl.).

Sitnik, S. M., Skoromnik, O. V., & Papkovich, M. V. (2022). Dva chastnykh sluchaya dvumernogo integral'nogo G-preobrazovaniya v vesovykh prostranstvakh summiruemykh funktsii [Two special cases of two-dimensional integral G-transformation in the weighted spaces of summable functions]. Vestnik Polotskogo gosudarstvennogo universiteta. Seriya C, Fundamental'nye nauki [Herald of Polotsk State University. Series С. Fundamental sciences], (11), 117–123. (In Russ., abstr. in Engl.). DOI: 10.52928/2070-1624-2022-39-11-117-123.

Skoromnik, O. V., & Papkovich, M. V. (2022). Mnogomernye modifitsirovannye G-preobrazovaniya i integral'nye preobrazovaniya s gipergeometricheskoi funktsiei Gaussa v yadrakh v vesovykh prostranstvakh summiruemykh funktsii [Multidimensional modified G-transformations and integral transformations with hypergeometric Gauss functions in kernels in weight spaces of summed functions]. Vesnіk Vіtsebskaga dzyarzhaunaga unіversіteta [Bulletin of VSU], 1(114), 11–25. (In Russ., abstr. in Engl.).

Sitnik S. M., Skoromnik, O. V., & Papkovich, M. V. (2022). Mnogomernye modifitsirovannye G- i H-preobrazovaniya i ikh chastnye sluchai [Multidimensional modified G- and H-transforms and their special cases]. In AMADE-2021: sb. trudov (104–116). Minsk: IVTs Minfina. (In Russ., abstr. in Engl.).

Sitnik, S. M., Skoromnik, O. V., & Shlapakov, S. A. (2019). Mnogomernoe obshchee integral'noe preobrazovanie so spetsial'nymi funktsiyami v yadre [Multidimensional general integral transformation with special functions in the kernel]. Vesnіk Vіtsebskaga dzyarzhaunaga unіversіteta [Bulletin of VSU], 3(104), 18–27. (In Russ., abstr. in Engl.).

Sitnik, S. M., & Skoromnik, O. V. (2020). One-dimensional and multi-dimensional integral transforms of Buschman-Erdelyi type with Legendre Functions in kernels. In Transmutation Operators and Applications. Trends in Mathematics (293–319). Cham, Switzerland: Birkhäuser Basel (Springer).

Samko, S. G., Kilbas, A. A., & Marichev, O. I. (1987). Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya [Integrals and derivatives of fractional order and some of their applications]. Minsk: Nauka i tekhnika. (In Russ.).

Beitmen, G., & Erdeii, A. (1973). Vysshie transtsendentnye funktsii: v 3 t. T. 1: Gipergeometricheskaya funktsiya Gaussa. Funktsiya Lezhandra. Moscow: Nauka. (In Russ.).

Kilbas, A. A., & Saigo, M. H. (2004). H-Transforms. Theory and Applications. London [etc.]: Chapman and Hall. CRC Press.

Sitnik, S. M., Skoromnik, O. V., & Shlapakov, S. A. (2022). Multi-dimensional generalized integral transform in the weighted spaces of summable functions. Lobachevskii J. of Mathematics, 43(6), 1170–1178.

Kilbas, A. A., Srivastava, H. M., & Trujillo, J. J. (Ed.). (2006). Theory and applications of fractional differential equations. North–Holland Mathematics Studies (Vol. 204). Amsterdam: Elsevier.xv.

Prudnikov, A. P., Brychkov, Yu. A., & Marichev, O. I. (1986). Integraly i ryady: v 3 t. T. 3: Dopolnitel'nye glavy. Moscow: Nauka. (In Russ.).