$\Psi_{K}\left(\mathbf{x}\right)=\dfrac{2}{K+2}\sum\limits_{n=0}^{\infty}\exp%
\left(i\dfrac{\pi(2n+1)}{2(K+2)}\right)\Gamma\left(\dfrac{2n+1}{K+2}\right)a_{%
2n}(\mathbf{x}),$