We study AAK-type meromorphic approximants to functions of the form F (z) = ∫ dλ(t ) z − t +R(z), where R is a rational function and λ is a complex measure with compact regular support included in (−1,1), whose argument has bounded variation on the support. The approximation is understood in Lp -norm of the unit circle, p ≥ 2. We dwell on the fact that the denominators of such approximants sati...

Applicability of the previously introduced method of modified diagonal Baker-Gammel approximants is extended to truncated perturbation series (TPS) of any order in gauge theories. The approximants reproduce the TPS when expanded in power series of the gauge coupling parameter to the order of that TPS. The approximants have the favorable property of being exactly invariant under the change of th...

The Padé table of 2F1(a, 1; c; z) is normal for c > a > 0 (cf. [4]). For m ≥ n−1 and c / ∈ Z − , the denominator polynomial Qmn(z) in the [m/n] Padé approximant Pmn(z)/Qmn(z) for 2F1(a, 1; c; z) and the remainder term Qmn(z)2F1(a, 1; c; z)−Pmn(z) were explicitly evaluated by Padé (cf. [2], [6] or [9]). We show that for c > a > 0 and m ≥ n−1, the poles of Pmn(z)/Qmn(z) lie on the cut (1,∞). We d...