Generating functions of the Zhang-Zhang polynomials of multiple zigzag chains Z(m; n) and generalized multiple zigzag chains Zκ(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)tm = [0;-T; (-1)2zt; (-1)3zt; ⋯ ; (-1)nzt; 1 + (-1)n+1zt]; or, in the case of Zκ(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.
|Number of pages||21|
|State||Published - Jan 2018|