Treffer: Some Extensions of M-Fractions Related to Strong Stieltjes Distributions: Some extensions of M-fractions related to strong Stieltjes distributions

Two-points Padé approximants correspondinq to series expansions at the origin and the point at infinity can be derived as convergents of suitable continued fractions now generally known as \(M\)-fractions [see \textit{J. H. Cabe}, J. Inst. Math. Appl. 15, 363-372 (1975; Zbl 0303.40003)]. The present paper studies even and odd extensions of these \(M\)-fractions [by an even (odd) extension of a continued fraction it should be understood a continued fraction whose even (odd) order convergents are the successive convergents of the original continued fraction] connected with the series expansions determined by strong Stieltjes distributions; in particular the so-called \(S^3[\omega,\beta,b]\) whose elements satisfy the symmetric property \[ d\psi(t)/t^\omega =-d\psi (\beta^2t^{-1})/ (\beta^2 t^{-1})^\omega \quad \text{where} \quad 0