On M\"untz-type formulas related to the Riemann zeta function

Abstract

The Mellin transform and several Dirichlet series related with the Riemann zeta function are used to deduce some identities similar to the classical M\"untz formula [4]. These formulas are derived in the critical strip and in the half-plane $Re(s)<0$. As particular cases, integral representations for products of the gamma and zeta functions are exhibited.