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<p>In this paper, by virtue of comparing coefficients and the technique of inverse relations, we establish some new generating functions of (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(q^{-1}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>q</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </math></EquationSource> </InlineEquation>-)Al-Salam-Carlitz polynomials which are in essence equivalent to the so-called bilinear forms. As applications of our methods, some new <i>q</i>-series identities related to the Al-Salam-Carlitz polynomials are presented.</p>

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Notes on the Al-Salam-Carlitz polynomials and allied q-identities

  • 期刊论文

  • 发表日期：

    2026年2月3日

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  • Qi Chen,
  • Jin Wang

摘要

In this paper, by virtue of comparing coefficients and the technique of inverse relations, we establish some new generating functions of ( \(q^{-1}\) q - 1 -)Al-Salam-Carlitz polynomials which are in essence equivalent to the so-called bilinear forms. As applications of our methods, some new q-series identities related to the Al-Salam-Carlitz polynomials are presented.