2025/03/14 by Arai, Yumi, Takemura, Kouichi
#33D15 #39A13 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · doi:10.48550/arxiv.2503.11214
We reformulate the q-convolution and the q-middle convolution introduced by Sakai and Yamaguchi, and we introduce q-deformations of the addition which is related to the gauge-transformation. A merit of the reformulation is the additivity on composition of two q-middle convolutions. We obtain sufficient conditions that the Jackson integrals associated with the q-convolution converge and satisfy the q-difference equation associated with the q-convolution. We present several third-order linear q-difference equations and solutions of them by using the q-middle convolution and the q-deformations of the addition.