Some \(q\)-Bernoulli numbers of higher order associated with the \(p\)-adic \(q\)-integrals
The authors define generalized higher \(q\)-Bernoulli numbers associated with Dirichlet characters. The construction is based on the notion of the \(p\)-adic \(q\)-integral of the Volkenborn type introduced by \textit{T. Kim} [J. Number Theory 76, 320--329 (1999; Zbl 0941.11048)]. An expression for generalized higher \(q\)-Bernoulli numbers via lower ones is found.
scientific article; zbMATH DE number 1785885