Some Generalized Harmonic Number Identities

Details Some Generalized Harmonic Number Identities Some Generalized Harmonic Number Identities

2011-03-28

arxiv.org/abs/1103.5430v2

Mathematics

Number Theory

Added examples, computer program and some textual corrections

Scientific paper

Summation by parts is used to find the sum of a finite series of generalized harmonic numbers involving a specific polynomial or rational function. The Euler-Maclaurin formula for sums of powers is used to find the sums of some finite series of generalized harmonic numbers involving nonnegative integer powers, which can be used to evaluate the sums of the finite series of generalized harmonic numbers involving polynomials. Many examples and a computer program are provided.

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