Solutions to q-hypergeometric equations associated with q-middle convolution

Abstract: We investigate the integral representations of solutions to q-hypergeometric equation and its variant obtained through q-middle convolution by using transformation formulas for q-hypergeometric series. We show the correspondence between these integral solutions and solutions obtained through other methods. We also show the linear relationships among the integral solutions. Specifically, we provide an alternative proof for the connection formula for the standard form of q-hypergeometric equation.