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<p>By employing two fundamental binomial transformation formulae, several binomial summation formulas involving Pell and Pell-Lucas polynomials are established. Notably, specific instances of these formulas yield intriguing identities involving Fibonacci/Lucas and Pell/Pell-Lucas numbers. In particular, this work offers innovative proofs for two identities introduced by Ohtsuka and Tauraso (2020), as well as a problem posed by Seiffert in 1995.</p>

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Binomial summation formulas involving Pell and Pell–Lucas polynomials

  • 期刊论文

  • 发表日期：

    2025年3月14日

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  • Yulei Chen,
  • Yanan Zhao,
  • Dongwei Guo

摘要

By employing two fundamental binomial transformation formulae, several binomial summation formulas involving Pell and Pell-Lucas polynomials are established. Notably, specific instances of these formulas yield intriguing identities involving Fibonacci/Lucas and Pell/Pell-Lucas numbers. In particular, this work offers innovative proofs for two identities introduced by Ohtsuka and Tauraso (2020), as well as a problem posed by Seiffert in 1995.