Communications of the
Korean Mathematical Society CKMS

The recent research investigates the generalization of Bessel function in different forms as its usefulness in various fields of applied sciences. In this paper, we introduce a new modified form of $k$-Bessel functions called the generalized modified $k$-Bessel functions and established some of its properties.

Keywords: $k$-Bessel functions, Gamma function, hypergeometric function $_{2}F_{1}$, generalized hypergeometric function $_{p}F_{q}$, generalized (Wright) hypergeometric functions $_{p}\Psi _{q}$

MSC numbers: 33C20, 33B15, 33C05, 33C10