Euler sums of generalized alternating hyperharmonic numbers

Sums over primes III

“…The conception of generalized alternating hyperharmonic numbers are introduced by the author [11] as an alternating analogue of the generalized hyperharmonic numbers H (p,r) n . Define the notion of the generalized alternating hyperharmonic numbers of types I, II, and III, respectively, as…”

“…The author [11] proved that the generalized alternating hyperharmonic numbers could be expressed as linear combinations of n's power times generalized (alternating) harmonic numbers.…”