261

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.

  • Ссылка в интернете
  • DOI10.56292/SJFSU/vol28_iss4/a38
  • Дата создание в систему UzSCI09-11-2022
  • Количество прочтений220
  • Дата публикации08-11-2022
  • Язык статьиRus
  • Страницы173-184
Ўзбек

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.

Русский

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.

English

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.
 

№ Имя автора Должность Наименование организации
1 Jalilov I.. 2 Fergana State University
2 Xasanov A.. 1 Tashkent Institute of Irrigation Engineers
№ Название ссылки
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.
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