Universal global analytic expansion for the 't Hooft-Polyakov monopole profiles

In this work we discuss in detail a global analytic expansion scheme for the solutions of the `t~Hooft-Polyakov monopole profile equations for arbitrary $\lambda/e^2>0$ based on the findings presented in a recent resurgence-oriented letter arXiv:2602.14620 [hep-th], which the present study significantly expands upon. A uniformly convergent functional perturbation series developed around universal, surprisingly simple, analytic non-perturbative background profiles corresponding to a partial resummation of the Borel-plane expansions suggested there, is constructed; a perfect match to what is known about the full solutions' local behaviour at zero and infinite radii is achieved, along with simple analytic prescriptions for the locally inaccessible numerical parameters therein.