  It is shown that if $\gamma$ is a path of finite $p$ variation ($1\leq p< 2$)
in a euclidean vector space and $f,g,h$ are Lipschitz functions on the trace of
$\gamma$ then $s\mapsto F(s)=\int_\gamma f^sg dh$ defines an entire holomorphic
function provided the convex hull of the image of $f$ does not contain zero. If
in addition $|\log z|\leq \log 2$ on the convex hull of the image of $f$ then
for any $s\in \mathbf{C}$, $F(s)$ can be computed from the nonnegative integer
values $\{F(k)\}_{k\in \mathbf{N}}$. If in addition to these hypotheses each of
$f,g,h$ is a polynomial, then the values $F(k)$ are computable directly from
the signature of $\gamma$ thus all values of $F(s)$ are computable from the
signature. As a special case the winding number of a closed path $\gamma$
around an affine submanifold of codimension two is computed from finitely many
terms of the signature provided certain estimates are satisfied.
