2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/185550In the preceding paper (Phys. Lett. B463 (1999) 257), the authors presented a q-analog of the ADHMN construction and obtained a family of anti-selfdual configurations with a parameter q for classical SU(2) Yang-Mills theory in four-dimensional Euclidean space. The family of solutions can be seen as a q-analog of the single BPS monopole preserving (anti-)selfduality. Further discussion is made on the relation to axisymmetric ansatz on anti-selfdual equation given by Witten in the late seventies. It is found that the q-exponential functions familiar in q-analysis appear as analytic functions categorizing the anti-selfdual configurations yielded by axisymmetric ansatz.11pages, Latex2e, to appear in Journal of Physics A: Mathematical and General as a `Special Issue/Difference Equations'High Energy Physics - Theorytext