Some Combinatorial Identities some of which involving Harmonic Numbers

Details Some Combinatorial Identities some of which involving Harmonic Numbers Some Combinatorial Identities some of which involving Harmonic Numbers

2011-03-07

arxiv.org/abs/1103.1268v1

Mathematics

Combinatorics

Scientific paper

A product difference equation is proved and used for derivation by elementary methods of four combinatorial identities, eight combinatorial identities involving generalized harmonic numbers and three combinatorial identities involving traditional harmonic numbers. For the binomial coefficients the definition with gamma functions is used, thus also allowing non-integer arguments in the identities. The generalized harmonic numbers in this case are harmonic numbers with a complex offset, where the traditional harmonic numbers are a special case with offset zero.

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