Figure 4

Logarithmic magnitude of the coefficients ${\mathit{A}}_{\mathit{p}\mathbf{,}\mathit{m}}$ and ${\mathit{B}}_{\mathit{p}\mathbf{,}\mathit{m}}$ ( $\mathit{p}\mathbf{=}\mathbf{1}\mathbf{,}\mathbf{2}$ ) relevant to the Fourier-Hankel series expansion ${\mathit{v}}_{\mathit{N}}\mathbf{(}\mathit{x}\mathbf{,}\mathit{y}\mathbf{)}$ representing the solution of the Robin problem for the Helmholtz equation in the supershaped annulus described by the Gielis formula with parameters ${\mathit{k}}_{\mathit{x}}^{\mathbf{\pm }}\mathbf{=}{\mathit{k}}_{\mathit{y}}^{\mathbf{\pm }}\mathbf{=}\mathbf{4}$ , ${\mathit{d}}_{\mathit{x}}^{\mathbf{-}}\mathbf{=}{\mathit{d}}_{\mathit{y}}^{\mathbf{-}}\mathbf{=}\mathbf{3}\mathbf{/}\mathbf{4}$ , ${\mathit{d}}_{\mathit{x}}^{\mathbf{+}}\mathbf{=}{\mathit{d}}_{\mathit{y}}^{\mathbf{+}}\mathbf{=}\mathbf{5}\mathbf{/}\mathbf{2}$ , ${\mathit{\nu }}_{\mathit{x}}^{\mathbf{\pm }}\mathbf{=}{\mathit{\nu }}_{\mathit{y}}^{\mathbf{\pm }}\mathbf{=}\mathbf{6}$ , ${\mathit{\nu }}_{\mathbf{0}}^{\mathbf{\pm }}\mathbf{=}\mathbf{10}$ .