Delayed Padé approximant convergent inside the unit circle

This chapter deals with delayed Padé approximant convergent inside the unit circle. The sum over k is an implicit quotient of two polynomials in the variable u and, hence, it is the Padé approximant. A special feature here is that the numerator polynomial has no free term independent of u. Thus, it is natural that the needed version of the delayed diagonal Padé approximant. The delayed Padé approximant with the convergence region inside the unit circle (|u| < 1) is identical to the even part of the delayed Lanczos continued fraction to any order n.