Please, is there a way to calculate this integral
$$\int_{S_{2n-1}} \frac{e^{a \langle z, \zeta \rangle}}{|z - \zeta|^{\beta}} \, d\sigma(\zeta)$$ where $ z $ is a fixed point in the complex unit ball $ \mathbb{C}^n $ and $\zeta $ is a point on the unit sphere $ S^{2n-1} $. The notation $ \langle z, \zeta \rangle $ denotes the Hermitian inner product, defined as:
$$\langle z, \zeta \rangle = \sum_{j=1}^{n} z_j \overline{\zeta_j},$$
where $\overline{\zeta_j}$ is the complex conjugate of $\zeta_j $. Thank you in advance
