Zhang-zhang polynomials of multiple zigzag chains

Generating functions of the Zhang-Zhang polynomials of multiple zigzag chains Z(m; n) and generalized multiple zigzag chains Z_κ(m; n) are derived for arbitrary values of the indices. These generating functions can be expressed in the form of highly regular finite continued fractions, Σ^∞ _m=0 ZZ(Z(m; n); z)t^m = [0;-T; (-1)²zt; (-1)³zt; ⋯ ; (-1)ⁿzt; 1 + (-1)ⁿ⁺¹zt]; or, in the case of Z_κ(m; n), products of such continued fractions. For the particularly important case of the multiple zigzag chains Z(m; n), the generating functions are expanded to yield a closed form for the Zhang-Zhang polynomials of multiple zigzag chains Z(m; n) that is valid for arbitrary values of m and n.