Pattern formation of poles and zeros of Padé Approximations for some functions with singularity

Padé approximants are a valuable tool for studying the singularity structure of analytical functions by analyzing the pattern formation of poles and zeros on the complex plane, derived from the Laurent series expansion. This technique is particularly useful for characterizing equations with elliptic solutions. However, in practical scenarios, functions of even modest complexity may exhibit anomalies, manifesting as unnecessary poles accompanied by adjacent zeros. Detecting these anomalies presents considerable challenges, but by discerning their transient behavior and disregarding approximations with anomalies near the origin, the authentic singularities of the function can be characterized. Copyright © 2023 Research India Publications.