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.  Not sure how to get latex to be processed.