Hello!

It may be a stupid question, i'm trying to find a closed form for an integral similar to a Fourier transform on $S^{n}$ but i'm stuck... Let $\alpha>0$, the integral i can't solve is

`$$I(p,\alpha)=\int_{S^{n}}e^{i\alpha\left<p,q\right>}d\mu_{S^{n}}(q)$$`

where $p,q\in S^{n}$, $\left< \cdot,\cdot \right>$ is the euclidean scalar product on $\mathbb{R}^{n+1}$ and $d\mu_{S^{n}}$ is the measure induced by euclidean measure on $\mathbb{R}^{n+1}$. so the question is: is there a closed form for $I(p,\alpha)$ only in terms of $p$ and $\alpha$?

Thank you in advance!