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Finite summation formulas involving binomial coefficients, harmonic numbers and generalized harmonic numbers. (English) Zbl 1283.11115

Summary: A variety of identities involving harmonic numbers and generalized harmonic numbers have been investigated since the distant past and involved in a wide range of diverse fields such as analysis of algorithms in computer science, various branches of number theory, elementary particle physics and theoretical physics. Here the author shows how one can obtain further interesting identities about certain finite series involving binomial coefficients, harmonic numbers and generalized harmonic numbers by applying the usual differential operator to a known identity.

MSC:

11M06 \(\zeta (s)\) and \(L(s, \chi)\)
33B15 Gamma, beta and polygamma functions
33E20 Other functions defined by series and integrals
11M35 Hurwitz and Lerch zeta functions
11M41 Other Dirichlet series and zeta functions
40C15 Function-theoretic methods (including power series methods and semicontinuous methods) for summability
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References:

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