# A singularity of hypergeometric functions

Do generalized hypergeometric functions $${}_p F_q(a_1,\ldots,a_p; b_1, \ldots,b_q; z)$$ with $p = q+1$ always possess a singularity at $z=1$, independent of the their parameters $a_1,\ldots,a_p$ and $b_1,\ldots,b_q$ under the provision that all cases of finite polynomials are excluded? Can someone mention a reliable source for such a statement or provide a counterexample?

For the $p=q+1$ case, taking the branch cut from 1 to ∞ is conventional so that you can speak of the principal branch of ${}_{q+1} F_q$ ; the function is multivalued outside the unit disk, and 1 and ∞ are branch points.