Abstract
This chapter discusses the combinatorial aspects of continued fractions. Usually divergent, power series have (formal) continued fractions expansions of a simple form. Almost all such continued fraction expansions can receive combinatorial proofs. The polynomials appearing in convergents of continued fractions satisfy certain formal orthogonality relations. The convergents of the continued fractions that can be interpreted combinatorially involve some of the classical polynomials: the Tchebycheff, Hermite, Laguerre, Meixner and Poisson–Charlier polynomials. Combinatorial interpretations for the Taylor coefficients of fractions involving these classical polynomials are discussed in the chapter.
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