On expansions involving the Riemann zeta function and its derivatives

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By studying the spectral aspects of the fractional part function in a well-known separable Hilbert space, we show, among other things, a rational approximation of the Riemann zeta function and its derivatives valid on every vertical line in the right half-planes ℜs>1/2 and ℜs>0. Moreover, we provide some discussions and explicit computations related to the fractional part function.