ABSTRACT
This chapter deals with the Lanczos continued fractions (LCF) and contracted continued fractions (CCF). A general CF, say C~(z), whose approximants coincide with a subset of the approximants of another continued fraction C(z) is called a contraction of C(z). The result shows that the approximant RnLCF(u) of order n of the LCF RLCF(u) is equal exactly to the approximant R2nCF(u) of order 2n of the continued fraction RCF(u). Thus, RCCF(u) is a contraction of RCF(u). Therefore, the PLA is equal to the LCF and to the CCF.
