В этой статье изучаются свойства функции Кампе де Фериет от двух аргументов четвертого порядка 2;2;2
0;3;3
F x, y . Доказаны интегральные представления и система дифференциальных уравнений в частных производных гипергеометрического типа, которую удовлетворяет указанная функция.
Ushbu maqolada ikki o‘zgaruvchili, to‘rtinchi tartibli F02;3;2;3;2 x, y Kampe de Feriyet funksiyasining integral ko‘rinishlari va bu funksiya qanoatlantiruvchi xususiy hosilali to‘rtinchi tartibli differensial tenglama sistemasi tuzilgan.
В этой статье изучаются свойства функции Кампе де Фериет от двух аргументов четвертого порядка 2;2;2
0;3;3
F x, y . Доказаны интегральные представления и система дифференциальных уравнений в частных производных гипергеометрического типа, которую удовлетворяет указанная функция.
This article studies the properties of the Kampe de Feriet function F02;3;2;3;2 ( x, y) of two fourth-order arguments.
Integral representations and a system of differential equations in partial derivatives of hypergeometric type, which is satisfied by the indicated function, are proved.
№ | Author name | position | Name of organisation |
---|---|---|---|
1 | Jalilov I.. | 2 | Fergana State University |
2 | Xasanov A.. | 1 | Tashkent Institute of Irrigation Engineers |
№ | Name of reference |
---|---|
1 | 1. P. Appell and Kampeґ de Feґriets, Fonctions Hypergeometriques et Hyperspheriques; Polynomes d’Hermite, Gauthier - Villars, Paris, 1926. |
2 | 2. J. Barros-Neto and I.M. Gelfand, Fundamental solutions for the Tricomi operator,Duke Math. J. 98(3) (1999), 465-483. |
3 | 3. J. Barros-Neto and I.M. Gelfand, Fundamental solutions for the Tricomi operator II, Duke Math. J. 111(3) (2002), 561-584. |
4 | 4. J. Barros-Neto and I.M. Gelfand, Fundamental solutions for the Tricomi operator III, Duke Math. J. 128(1) (2005), 119-140. |
5 | 5. L. Bers, Mathematical Aspects of Subsonic and Transonic Gas Dynamics, Wiley, New York, 1958. |
6 | 6. A. Erde’lyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher Transcendental Functions, Vol. 1, McGraw-Hill Book Company, New York, Toronto and London, 1953. |
7 | 7. F.I. Frankl, Selected Works in Gas Dynamics, Nauka, Moscow, 1973. |
8 | 8. A.J. Fryant, Growth and complete sequences of generalized bi-axially symmetric potentials, J. Differential Equations 31(2) (1979), 155-164. |
9 | 9. Junesang Choi, Anvar Hasanov and Mamasali Turaev, Linear independent solutions for the hypergeometric Exton function, Honam Mathematical J. 33 (2011), No. 2, pp. 223-229. |
10 | 10. A. Hasanov, Fundamental solutions of generalized bi-axially symmetric Helmholtz equation, Complex Variables and Elliptic Equations 52(8) (2007), 673-683. |
11 | 11. A. Hasanov, Some solutions of generalized Rassias’s equation, Intern. J. Appl. Math. Stat. 8(M07) (2007), 20-30. |
12 | 12. A. Hasanov, The solution of the Cauchy problem for generalized Euler-Poisson- Darboux equation. Intern. J. Appl. Math. Stat. 8 (M07) (2007), 30-44. |
13 | 13. A. Hasanov, Fundamental solutions for degenerated elliptic equation with two perpendicular lines of degeneration. Intern. J. Appl. Math. Stat. 13(8) (2008), 41-49. |
14 | 14. A. Hasanov and E.T. Karimov, Fundamental solutions for a class of three-dimensional elliptic equations with singular coefficients. Appl. Math. Letters 22 (2009), 1828-1832. |
15 | 15. Hasanov, J.M. Rassias , and M. Turaev, Fundamental solution for the gen- eralized Elliptic Gellerstedt Equation, Book: "Functional Equations, Difference Inequalities and ULAM Stability Notions Nova Science Publishers Inc. NY, USA, 6 (2010), 73-83. |
16 | 16. Anvar Hasanov, Rakhila B. Seilkhanova and Roza D. Seilova, Linearly independent solutions of the system of hypergeometric Exton function, Contemporary Analysis and Applied Mathematics Vol.3, No.2, 289-292, 2015 |
17 | 17. G. Lohofer, Theory of an electro-magnetically deviated metal sphere. 1: Absorbed power, SIAM J. Appl. Math. 49 (1989), 567-581. |
18 | 18. A.W. Niukkanen. Generalized hyper-geometric series arising in physical and quantum chemical applications, J. Phys. A: Math. Gen. 16 (1983) 1813-1825. |
19 | 19. H. M. Srivastava and P. W. Karlsson, Multiple Gaussian hyper-geometric Series, Halsted Press (Ellis Horwood Limited, Chichester), Wiley, New York, Chichester, Brisbane, and Toronto, 1985. |
20 | 20. R.J. Weinacht, Fundamental solutions for a class of singular equations, Contrib. Differential Equations 3 (1964), 43-55. |
21 | 21. A. Weinstein, Discontinuous integrals and generalized potential theory, Trans. Amer. Math. Soc. 63 (1946), 342-354. |