M. J. Kronenburg
Published 2011-03-07, updated 2015-11-10Version 2
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 classical 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 classical harmonic numbers are a special case with offset zero.
Comments: Added equations (4.27), (4.28) and (4.29)
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