Continued fractions and q-series generating functions for the generalized sum-of-divisors functions

摘要

Abstract We construct new continued fraction expansions of Jacobi-type J-fractions in z whose power series expansions generate the ratio of the q-Pochhammer symbols, ( a ; q ) n / ( b ; q ) n , for all integers n ≥ 0 and where a , b , q ∈ C are non-zero and defined such that | q | 1 and | b / a | | z | 1 . If we set the parameters ( a , b ) : = ( q , q