Delayed Padé approximant convergent outside the unit circle

This chapter deals with delayed Padé approximant convergent outside the unit circle. Our starting point of the analysis is the exact delayed Green function. The chapter shows how to determine the unknown expansion coefficients ar(s)^- and br(s)^- by imposing the equality GN(s)(u-1)=GKPA(s)-(u-1). The delayed Padé approximant with the convergence region outside the unit circle (|u| > 1) is identical to the odd part of the delayed Lanczos continued fraction to any order n.