Generalization of identities involving complex parameters shows applications in polynomial and trigonometric identities, highlighting richness in combinatorial applications.
Inspired by a problem proposal recently published in the journal The Fibonacci Quarterly we offer a generalization consisting of two combinatorial identities involving three complex parameters. These identities turn out to be immensely rich. We demonstrate this by providing basic applications to four different fields: polynomial identities, trigonometric identities, identities involving Horadam numbers, and combinatorial identities. Many of our findings will generalize existing results.
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Adegoke et al. (2025) studied this question.
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