Weighted error-sum identities for periodic continued fractions and their generalizations

Kevin Calderon, Nikita Kalinin

For a purely $N$-periodic continued fraction $\xi =[\overline{a_0,a_1,\dots ,a_{N-1}}]=[a_0,a_1,\cdots ]$, with $a_k=a_{k+N}$ for all $k\ge 0$, and convergents $h_n/k_n=[a_0,a_1,\dots,a…