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Some debts I owe.

Andrews, George E. (1999)

Séminaire Lotharingien de Combinatoire [electronic only]

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 interpretations of the ( k , p ) -Fibonacci numbers

Natalia Paja, Iwona Włoch (2021)

Commentationes Mathematicae Universitatis Carolinae

In this paper we consider two parameters generalization of the Fibonacci numbers and Pell numbers, named as the ( k , p ) -Fibonacci numbers. We give some new interpretations of these numbers. Moreover using these interpretations we prove some identities for the ( k , p ) -Fibonacci numbers.

Some new transformations for Bailey pairs and WP-Bailey pairs

James Mc Laughlin (2010)

Open Mathematics

We derive several new transformations relating WP-Bailey pairs. We also consider the corresponding transformations relating standard Bailey pairs, and as a consequence, derive some quite general expansions for products of theta functions which can also be expressed as certain types of Lambert series.

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