The operator equation ∑i=0nAn-iXBi=Y

The solution of the linear operator equation:An-1X+An-2XB+⋯+AXBn-2+XBn-1=YAn-1X+An-2XB+⋯+AXBn-2+XBn-1=Y is given by X=((sinπ/n)/π)∫0∞(t+An)-1Y(t+Bn)-1t1/ndt if the spectra of A and B   are in the sector {z:z≠0,-π/n