In 1976, Chisholm et al. 1 published a paper concerning the location of poles and zeros of Padé approximants of ln 1 − z developed at the complex point ζ : ln 1 − z ln 1 − ζ − ∑∞ n 1 1/n z − ζ/1 − ζ . They claimed that all poles and zeros of diagonal Padé approximants n/n interlace on the cut z ζ t 1 − ζ , t ∈ 1,∞ . Unfortunately, this result is only partially true, for poles. Klarsfeld remarke...

Wide-angle scalar beam propagation methods (BPMs) for effective modelling of optical propagation in three-dimensional (3D) waveguides are usually limited to the low-order-accurate Padé(1,1) approximant. Presented is a 3D wide-angle scalar BPM based on higher-order Padé approximant operators which is factored into a series of simpler first-order Padé(1,1) approximants. This results in a multiste...

We classify all integer squares (and, more generally, q-th powers for certain values of q) whose ternary expansions contain at most three digits. Our results follow from Padé approximants to the binomial function, considered 3-adically.