A sequence inverse relationship can be defined by a pair of infinite inverse matrices. If those two matrices are the same, they define a dual relationship. Presented here is a unified approach to construct dual relationships using pseudo-Riordan involutions. Then we give four dual relationships for the Bernoulli numbers and the Euler numbers, from which the corresponding dual sequences of the Bernoulli polynomials and the Euler polynomials are constructed. Some applications in the construction of identities of the Bernoulli numbers and polynomials and the Euler numbers and polynomials are discussed based on the dual relationships.
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