Transcendence of $p$-adic values of generalized hypergeometric series with transcendental polyadic parameters

It is established that if $\alpha_1,\dots,\alpha_m$ are polyadic Liouville numbers, and the number $\xi$ is a positive integer or $\Xi$ is a polyadic Liouville number and if $\Psi_0(z)=\sum_{n=0}^\infty(\alpha_1)_n\cdots(\alpha_m)_nz^n$, $\Psi_1(z)=\sum_{n=0}^\infty(\alpha_1+1)_n\cdots(\alpha_m+1)_nz^n$, then there are infinitely many primes $p$ such that the at least one of the $p$-adic integers $\Psi_0(\xi)$, $\Psi_1(\xi)$, (respectively $\Psi_0(\Xi)$, $\Psi_1(\Xi)$) is transcendental.