SplitSymbolicPowers is an option for
FCFeynmanParametrize and other functions. When set to
True, propagator powers containing symbols will be split
into a nonnegative integer piece and the remaining piece. This leads to
a somewhat different form of the resulting parametric integral, although
the final result remains the same. The default value is
False.
Overview, FCFeynmanParametrize.
SFAD[{p, m^2, r + 2}](p^2-m^2+i \eta )^{-r-2}
v1 = FCFeynmanParametrize[SFAD[{p, m^2, r - 1}], {p}, Names -> x, FCReplaceD -> {D -> 4 - 2 Epsilon}]\left\{1,\frac{m^6 (-1)^{r-1} \left(m^2\right)^{-\varepsilon -r} \Gamma (\varepsilon +r-3)}{\Gamma (r-1)},\{\}\right\}
v2 = FCFeynmanParametrize[SFAD[{p, m^2, r - 1}], {p}, Names -> x, FCReplaceD -> {D -> 4 - 2 Epsilon},
SplitSymbolicPowers -> True]\left\{1,\frac{m^6 (-1)^{r-1} (r-1) \left(m^2\right)^{-\varepsilon -r} \Gamma (\varepsilon +r-3)}{\Gamma (r)},\{\}\right\}
Both parametrizations lead to the same results (as expected)
Series[v1[[2]], {Epsilon, 0, 1}] // Normal
Series[v2[[2]], {Epsilon, 0, 1}] // Normal
% - %% // Simplify // FunctionExpand\frac{\varepsilon m^6 (-1)^r \left(m^2\right)^{-r} \Gamma (r-3) \left(\log \left(m^2\right)-\psi ^{(0)}(r-3)\right)}{\Gamma (r-1)}-\frac{m^6 (-1)^r \left(m^2\right)^{-r} \Gamma (r-3)}{\Gamma (r-1)}
\frac{\varepsilon m^6 (-1)^r (r-1) \left(m^2\right)^{-r} \Gamma (r-3) \left(\log \left(m^2\right)-\psi ^{(0)}(r-3)\right)}{\Gamma (r)}-\frac{m^6 (-1)^r (r-1) \left(m^2\right)^{-r} \Gamma (r-3)}{\Gamma (r)}
0