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O‘zbekcha

INTEGRAL REPRESENTATIONS AND THE SYSTEM OF DIFFERENTIAL EQUATION OF HYPERGEOMETRIC TYPE IN PARTIAL DERIVATIVES OF THE FOURTH ORDER FOR A FUNCTION

Authors

  • Институт математики, Ташкент, Узбекистан, Институт механики и сейсмостойкости сооружений, Ташкент, Узбекистан
  • Fergana state unversity

Keywords:

Hypergeometric functions of several variables, integral representations, system of equations of hypergeometric type.

Abstract

This article studies the properties of the Kampe de Feriet function  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 Biographies

  • , Институт математики, Ташкент, Узбекистан, Институт механики и сейсмостойкости сооружений, Ташкент, Узбекистан

    доктор физ.-мат. наук, профессор Институт математики, Ташкент, Узбекистан, Институт механики и сейсмостойкости сооружений, Ташкент, Узбекистан,

  • , Fergana state unversity

    Ферганский гос. университет, Фергана, Узбекистан

References

P. Appell and Kampeґ de Feґriets, Fonctions Hypergeometriques et Hyperspheriques; Polynomes d’Hermite, Gauthier - Villars, Paris, 1926.

J. Barros-Neto and I.M. Gelfand, Fundamental solutions for the Tricomi operator,Duke Math. J. 98(3) (1999), 465-483.

J. Barros-Neto and I.M. Gelfand, Fundamental solutions for the Tricomi operator II, Duke Math. J. 111(3) (2002), 561-584.

J. Barros-Neto and I.M. Gelfand, Fundamental solutions for the Tricomi operator III, Duke Math. J. 128(1) (2005), 119-140.

L. Bers, Mathematical Aspects of Subsonic and Transonic Gas Dynamics, Wiley, New York, 1958.

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.

F.I. Frankl, Selected Works in Gas Dynamics, Nauka, Moscow, 1973.

A.J. Fryant, Growth and complete sequences of generalized bi-axially symmetric potentials, J. Differential Equations 31(2) (1979), 155-164.

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.

A. Hasanov, Fundamental solutions of generalized bi-axially symmetric Helmholtz equation, Complex Variables and Elliptic Equations 52(8) (2007), 673-683.

A. Hasanov, Some solutions of generalized Rassias’s equation, Intern. J. Appl. Math. Stat. 8(M07) (2007), 20-30.

A. Hasanov, The solution of the Cauchy problem for generalized Euler-Poisson- Darboux equation. Intern. J. Appl. Math. Stat. 8 (M07) (2007), 30-44.

A. Hasanov, Fundamental solutions for degenerated elliptic equation with two perpendicular lines of degeneration. Intern. J. Appl. Math. Stat. 13(8) (2008), 41-49.

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.

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.

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

G. Lohofer, Theory of an electro-magnetically deviated metal sphere. 1: Absorbed power, SIAM J. Appl. Math. 49 (1989), 567-581.

A.W. Niukkanen. Generalized hyper-geometric series arising in physical and quantum chemical applications, J. Phys. A: Math. Gen. 16 (1983) 1813-1825.

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.

R.J. Weinacht, Fundamental solutions for a class of singular equations, Contrib. Differential Equations 3 (1964), 43-55.

A. Weinstein, Discontinuous integrals and generalized potential theory, Trans. Amer. Math. Soc. 63 (1946), 342-354.

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Published

2022-08-25