On convergence criteria for branched continued fraction
The starting point of the present paper is a result by E.A. Boltarovych (1989) on convergence regions, dealing with branched continued fraction \[_i_1=1^Na_i(1) 1+_i_2=1^Na_i(2) 1+…+_i_n=1^Na_i(n) 1+…,\] where |a_i(2n-1)|α/N, i_p=1,N, p=1,2n-1, n1, and for each multiindex i(2n-1) there is a single index j_2n, 1j_2nN, such that |a_i(2n-1),j_2n |R, i_p=1,N, p=1,2n-1, n1, and |a_i(2n)|r/(N-1), i_2n e j_2n, i_p=1,N, p=1,2n, n1, where N>1 and α, r and R are real numbers that satisfying certain conditions. In the present paper conditions for these regions are replaced by _i_1=1^N|a_i(1)|α(1-ε), _i_2n+1=1^N|a_i(2n+1)|α(1-ε), i_p=1,N, p=1,2n, n1, and for each multiindex i(2n-1) there is a single index j_2n, 1j_2nN, such that |a_i(2n-1),j_2n |R and _i_2n{1,2,…,N}{j_2n |a_i(2n)|r, i_p=1,N, p=1,2n-1, n1, where ε, α, r and R are real numbers that satisfying certain conditions, and better convergence speed estimates are obtained. , number=1, journal=Carpathian Mathematical Publications, author=Antonova, T.M., year=2020, month=Jun., pages=157–164