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.