(untitled) (European Journal of Pure and Applied Mathematics, 2021)
For the first time, the general properties of degenerate related hypergeometric systems such as Horn, Whittaker, Bessel and Laguerre are investigated together. The joint research allowed to reveal their various common properties and to establish a number of new degenerate related systems. They are all private cases of the common system offered by the authors for consideration. For the full study, it is important to classify its regular and irregular special curves and to identify the types of corresponding solutions. In this paper, they are implemented using simple rules. Special attention is paid to the construction of normal and regular solutions, because the solutions of all related degenerate systems such as Horn, Whittaker, Bessel and Laguerre near the irregular singularity on infinity relate to this species. Peculiarities of building normal-regular solutions by the Frobenius-Latysheva method are shown. All constructed normal-regular solutions are expressed through the function of Humbert Â variables, which is the solution of degenerate hypergeometric system of Horn type. As an example, the cases Â where, along with the application of the Frobenius-Latysheva method, the possibility of outputting new degenerate related systems is demonstrated.