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Various new identities, recurrence relations, integral representations, connection and explicit formulas are established for the Bernoulli and Euler numbers and the values of Riemann's zeta function ζ( s ). To do this, we explore properties of some Sheffer's sequences of polynomials related to the Kontorovich–Lebedev transform.

Certain identities, connection and explicit formulas for the Bernoulli and Euler numbers and the Riemann zeta-values