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Some extensions of Chu's formulas and further combinatorial identities

Said Zriaa, Mohammed Mouçouf (2024)

Mathematica Bohemica

We present some extensions of Chu's formulas and several striking generalizations of some well-known combinatorial identities. As applications, some new identities on binomial sums, harmonic numbers, and the generalized harmonic numbers are also derived.

Some finite generalizations of Euler's pentagonal number theorem

Ji-Cai Liu (2017)

Czechoslovak Mathematical Journal

Euler's pentagonal number theorem was a spectacular achievement at the time of its discovery, and is still considered to be a beautiful result in number theory and combinatorics. In this paper, we obtain three new finite generalizations of Euler's pentagonal number theorem.

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