Abstract
Particular cases of a special system of partial differential equations whose solutions are representable in the form of special functions and orthogonal polynomials in two variables are studied.
Literature cited
K. Ya. Latysheva and N. I. Tereshchenko, Lectures on the Analytic Theory of Differential Equations and Their Applications. The Frobenius-Latysheva Method [in Russian], Inst. Mat. Akad. Nauk Ukr. SSR, Kiev (1970).
Zh. N. Tasmambetov, “On a finite solution of a certain special system of second-order partial differential equations,” in: Analytical and Numerical Methods of Solving Problems of Mathematics and Mechanics [in Russian], Nauka, Alma-Ata (1984), pp. 145–149.
A. M. Samoilenko, N. A. Perestyuk, and Zh. N. Tasmambetov, “Solutions in finite form of a regular system of partial differential equations,” Preprint Inst. Mat. Akad. Nauk Ukr. SSR No. 90.21, Kiev (1990).
Zh. N. Tasmambetov, “On the determination of the regular singularities of a certain partial differential system,” Izv. Akad. Nauk Kazakh. SSR, Ser. Fiz.-Mat., No. 3, 50–53 (1988).
Zh. N. Tasmambetov,“Irregular singularities of a certain special system of second-order partial differential equations,” Vestn. Kiev. Univ., No. 32, 132–136 (1990).
N. I. Tereshchenko and Zh. N. Tasmambetov, “On the rank of a system of second-order partial differential equations,” Izv. Akad. Nauk Kazakh. SSR, Ser. Fiz.-Mat., No. 5, 72–78 (1972).
P. Appell and M. G. Kampede Feriet, Functions Hypergeometriques of Hyperspheres. Polynomes d'Hermite, Gauthier-Villars, Paris (1926).
M. K. Suetin, Orthogonal Polynomials in Two Variables [in Russian], Nauka, Moscow (1988).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 3, pp. 427–430, March, 1992.
Rights and permissions
About this article
Cite this article
Tasmambetov, Z.N. A Certain system of second-order partial differential equations. Ukr Math J 44, 371–375 (1992). https://doi.org/10.1007/BF01063140
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01063140