Power series expansions for Mathieu functions with small arguments

Power series expansions for the even and odd angular Mathieu functions Se m ⁡ ( h , cos ⁡ θ ) Se_m(h,cosθ ) and So m ⁡ ( h , cos ⁡ θ ) So_m(h,cosθ ) , with small argument h h , are derived for general integer values of m m . The expansion coefficients that we evaluate are also useful for the calculation of the corresponding radial functions of any kind.