Confluent Kampé de Fériet Series Arising in the Solutions of Cauchy Problem for the Degenerate Hyperbolic Equation of the Second Kind with the Spectral Parameter
Maged G. Bin-SaadDepartment of Mathematics, Aden University, Aden, YemenTuhtasin ErgashevNational Research University “Tashkent Institute of Irrigation and Agricultural Mechanization Engineers”, 39, Kari-Niyazi Street, Tashkent, 100000, UzbekistanDildora A. ErgashevaNational Research University “Tashkent Institute of Irrigation and Agricultural Mechanization Engineers”, 39, Kari-Niyazi Street, Tashkent, 100000, UzbekistanAnvarjon HasanovInstitute of Mathematics, 4 University Street, Tashkent, Uzbekistan
ABI
Abstract
We define the order of the double hypergeometric series, investigate the properties of the new confluent Kampé de Fériet series, and build systems of partial differential equations that satisfy the new Kampé de Fériet series. We solve the Cauchy problem for a degenerate hyperbolic equation of the second kind with a spectral parameter using the high-order Kampé de Fériet series. Thanks to the properties of the introduced Kampé de Fériet series, it is possible to obtain a solution to the problem in explicit forms.
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