Special Issue Editorial: Theory and Applications of Special Functions II

This Editorial introduces the Symmetry Special Issue “Theory and Applications of Special Functions II” and summarizes the nine contributions collected therein. The papers span the analytic continuation of multivariate hypergeometric functions; stability theory for differential equations via integral transforms; numerical schemes for multi-space fractional partial differential equations based on nonstandard finite differences and orthogonal polynomials; applications of the Lambert W function to viscoelastic creep modeling; algebraic constructions of new Hermite-type polynomial families via the monomiality principle; higher-level generalizations of poly-Cauchy numbers; Bell-polynomial expansions for Laplace transforms of higher-order nested functions; and two complementary studies on the physical implementation and algebraic description of Gaussian quantum states. Beyond the contributions of the Special Issue, we highlight methodological connections—continued fractions and complex analysis, transform techniques, special polynomials, and combinatorial sequences—and emphasize the unifying role of symmetry across mathematical structures and applications.