Asymptotic formulas for the determinants of symmetric Toeplitz + Hankel   matrices
  We establish asymptotic formulas for the determinants of finite Toeplitz + Hankel matrices of size N, as N goes to infinity for singular generating functions defined on the unit circle in the special case where the generating function is even, i.e., where the Toeplitz + Hankel matrices are symmetric. 
Estelle L. Basor and Torsten Ehrhardt