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 Ξ is a polyadic Liouville number and if ${\mathrm{\Psi }}_0\left(z\right)=\sum _{n=0}^{\mathrm{\infty }}{\left({\alpha }_1\right)}_n\dots {\left({\alpha }_m\right)}_n{z}^n,$ ${\mathrm{\Psi }}_1(z)=\sum _{n=0}^{\mathrm{\infty }}{\left({\alpha }_1+1\right)}_n\dots {\left({\alpha }_m+1\right)}_n{z}^n$, then there are infinitely many primes p such that the at least one of the p-adic integers ${\mathrm{\Psi }}_0\left(\xi \right),$ ${\mathrm{\Psi }}_1\left(\xi \right)$ (respectively, ${\mathrm{\Psi }}_0\left(\text{Xi }\right)),$ ${\mathrm{\Psi }}_1\left(\text{Xi }\right)$ is transcendental.