When is the $I$-Bessel function an algebraic integer?

Question

Is there any way to determine if the $I$-Bessel function $I_{a}(x)$ is an algebraic integer whenever $a \in \mathbb{N}$ and $x$ is an algebraic integer?

I have tried to search other papers on this topic, but almost all of them are analytic results on $I_{a}(x)$. At least a push in the right direction would be much appreciated.

Answer 1

For example, $I_1(2)/I_0(2)$ is known to be transcendental (Siegel 1929). Therefore $I_1(2)$ and $I_0(2)$ can't both be algebraic numbers.