  For a hyperelliptic curve of genus $g$, it is well known that the symmetric
products of $g$ points on the curve are expressed in terms of their Abel-Jacobi
image by the hyperelliptic sigma function (Jacobi inversion formulae).
Matsutani and Previato gave a natural generalization of the formulae to the
more general algebraic curves defined by $y^r=f(x)$, which are special cases of
$(n,s)$ curves, and derived new vanishing properties of the sigma function of
the curves $y^r=f(x)$. In this paper we extend the formulae to the telescopic
curves proposed by Miura and derive new vanishing properties of the sigma
function of telescopic curves. The telescopic curves contain the $(n,s)$ curves
as special cases.
