  For a self-repelling polymer chain consisting of n segments we calculate the
persistence length L(j,n), defined as the projection of the end-to-end vector
on the direction of the j`th segment. This quantity shows some pronounced
variation along the chain. Using the renormalization group and
epsilon-expansion we establish the scaling form and calculate the scaling
function to order epsilon^2. Asymptotically the simple result L(j,n) ~
const(j(n-j)/n)^(2nu-1) emerges for dimension d=3. Also outside the excluded
volume limit L(j,n) is found to behave very similar to the swelling factor of a
chain of length j(n-j)/n. We carry through simulations which are found to be in
good accord with our analytical results. For d=2 both our and previous
simulations as well as theoretical arguments suggest the existence of
logarithmic anomalies.
