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