Given a function $F(z)$, the function $F(z-m)$ is called
the Taylor shift of $F(z)$.  If $F(z)$ is a (general) hypergeometric
function, is $F(z-m)$ some simple transformation of a hypergeometric
function.  Typical transforms of $F(z)$ are $A(z) F(B(z))$
where $A(z), B(z)$ are polynomials.

More precisely, suppose 
$F(z)={}_pF_q((a);(b);z)$ where $(a),(b)$ are the parameters,
is $F(z-m)$ is some simple transformation
of a hypergeometric function.

For example, $F(z)={}_1F_0(a;;z)$, I can show that
    $$F(z-m) = (1+m)^{-a} F\big(\frac{x}{1+m}\big)$$
Taylor shift is very important for efficient algorithms.
Also, any pointers or references would be appreciated.
This is my first question in mathoverflow.