On (i,q)(i,q) Bernoulli and Euler numbers

The pp-adic invariant qq-integral on ZpZp was originally constructed by T. Kim [T. Kim, On a qq-analogue of the pp-adic log gamma function and related integrals, J. Number Theory 76 (1999) 320–329]. Recently, many authors have been studying the extended Bernoulli numbers or Euler numbers by using this pp-adic qq-integral in the fermionic or bosonic sense. Let i∈OCp={x∈Cp:|x|p⩽1}. Then we consider new (i,q)(i,q)-Bernoulli and Euler numbers using pp-adic qq-integrals in this work.