28 Mathieu Functions and Hill’s EquationModified Mathieu Functions28.26 Asymptotic Approximations for Large $q$28.28 Integrals, Integral Representations, and Integral Equations

Addition theorems provide important connections between Mathieu functions with different parameters and in different coordinate systems. They are analogous to the addition theorems for Bessel functions (§10.23(ii)) and modified Bessel functions (§10.44(ii)). For a comprehensive treatment see Meixner et al. (1980, §2.2).