Abstract:In this paper, we consider meromorphic extension of the function(which we call hyperharmonic zeta function) where h (r) n are the hyperharmonic numbers. We establish certain constants, denoted γ h (r) (m), which naturally occur in the Laurent expansion of ζ h (r) (s). Moreover, we show that the constants γ h (r) (m) and integrals involving generalized exponential integral can be written as a finite combination of some special constants.
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