On the Mellin–Barnes integral representation of one special function

The paper considers the Mellin–Barnes integral representation of a special function that arises in the theory of boundary value problems for parabolic equations with a Bessel operator and a fractional time derivative. The convergence of such an integral is investigated. The expansion of the considered function into power series and asymptotic formulas for large and small values of the argument is given. For particular values of the parameters of the function under consideration, some well-known elementary and special functions are obtained.