Adyghe Int. Sci. J. Vol. 22, No 2. P. 34-40. ISSN 1726-9946
Read article Contents of this issue
DOI: https://doi.org/10.47928/1726-9946-2022-22-2-34-40
MATHEMATICS
MSC 32A10; 32A37 | Original Article |
On some properties of one special function
Fatima Gidovna Khushtova
Researcher of Department of Fractional Calculus, Institute of Applied Mathematics and Automation of KBSC RAS, (360017, 89 А Shortanova St., Nalchik, Russia), Ph.D., http://orcid.org/0000-0003-4088-3621, khushtova@yandex.ru
Abstract. In the paper, some properties of one particular case of the special Fox function are studied. In particular, an autotransformation formula and its integral representation for some parameters are obtained. The Mellin transform formula is given. In terms of the function under study, solutions to boundary value problems for a differential equation with a Bessel operator acting with respect to a spatial variable and a partial derivative of a fractional order with respect to a time variable were previously written out. When proving the results obtained, the well-known properties of the Euler gamma function, the Wright function, and the properties of the Mellin transform were used.
Keywords: Fox function, Wright function, Euler gamma function, Mellin transform, Mellin convolution
Acknowledgments: the author are thankful to the anonymous reviewer for his valuable remakes.
For citation. F.~G. Khushtova On some properties of one special function. Adyghe Int. Sci. J. 2022. Vol. 22, No. 2. P. 34–40. DOI: https://doi.org/10.47928/1726-9946-2022-22-2-34-40
The author has read and approved the final version of the manuscript.
Submitted 24.06.2022; approved after reviewing 01.07.2022; accepted for publication 04.07.2022.
© Хуштова Ф. Г., 2022
REFERENCES
1. D. S. Kuznecov Special’nye funkcii. M.: Vysshaja shkola, 1962. 248 p.
2. G. Bejtmen, A. Jerdeji Vysshie transcendentnye funkcii. T. I. M.: Nauka, 1965. 296 p.
3. E. M. Wright On the coefficients of power series having exponential singularities. Journal of the London Mathematical Society. 1933. V. 8, No. 1. 71–79.
4. E. M. Wright The generalized Bessel function of order greater than one. The Quarterly Journal of Mathematics. 1940. V. os-11, No. 1, pp. 36–48.
5. B. Stanković}On the function of E. M. Wright. Publications de l Institut Mathematique. 1970. V.~10 (24). pp. 113–124.
6. A. P. Prudnikov, Ju. A. Brychkov, O. I. Marichev Integraly i rjady. T. 3. Dopolnitel’nye glavy. M.: Nauka, 1986. 800 p.
7. А. A. Kilbas, M. Saigo H-Transform. Theory and Applications. Chapman and Hall/CRC, Boca Raton, London, New York and Washington, D.C. 2004, 389 p.
8. A. M. Mathai, R. K. Saxena, H. J. Haubold The H-function. Theory and Applications. Springer. New York, 2010. 270 p.
9. F. G. Khushtova Formuly differentsirovaniya i formula avtotransformatsii dlya odnogo chastnogo sluchaya funktsii Foksa. Doklady AMAN. 2020. T. 20, No. 4. pp. 15–18.
10. F. G. Khushtova Pervaya kraevaya zadacha v polupolose dlya uravneniya parabolicheskogo tipa s operatorom Besselya i proizvodnoy Rimana–Liuvillya. Matematicheskie zametki. 2016. T. 99, vyp. 6. pp. 921–928.
11. F. G. Khushtova Vtoraya kraevaya zadacha v polupolose dlya uravneniya parabolicheskogo tipa s operatorom Besselya i chastnoy proizvodnoy Rimana–Liuvillya. Matematicheskie zametki. 2018. T. 103, vyp. 3. pp. 460–470.
12. O. I. Marichev Metod vychisleniya integralov ot spetsial’nykh funktsiy (teoriya i tablitsy formul). Mn.:
Nauka i tekhnika, 1978. 312 p.
13. A. V. Pskhu Uravneniya v chastnykh proizvodnykh drobnogo poryadka. M.: Nauka, 2005. 199 p.
This work is licensed under a Creative Commons Attribution 4.0 License.