q-MULTIPARAMETER-BERNOULLI POLYNOMIALS AND q-MULTIPARAMETER-CAUCHY POLYNOMIALS BY JACKSON’S INTEGRALS

摘要

We define q-multiparameter-Bernoulli polynomials and q-multiparameter-Cauchy polynomials by using Jackson’s integrals, which generalize the previously known numbers, including poly-Bernoulli B(k) n and the poly-Cauchy numbers of the first kind c (k) n and of the second kind bc (k) n . We investigate their properties connected with multiparameter Stirling numbers which generalize the original Stirling numbers. We also give the relations between q-multiparameter-Bernoulli polynomials and qmultiparameter-Cauchy polynomials.