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<p>In this paper, using the technique of comparing coefficients, we establish a new <i>q</i>-series transformation connecting the Jacobi triple product identity with the Al-Salam-Carlitz polynomials. As further application of our argument, we introduce the multivariate Al-Salam-Carlitz polynomials and establish its bilinear generating function. Other special <i>q</i>-series transformations are also presented.</p>

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A new connection of the Al-Salam-Carlitz polynomials with the Jacobi triple product identity and its implications

  • 期刊论文

  • 发表日期：

    2026年1月19日

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  • Qi Chen,
  • Xinrong Ma,
  • Jin Wang

摘要

In this paper, using the technique of comparing coefficients, we establish a new q-series transformation connecting the Jacobi triple product identity with the Al-Salam-Carlitz polynomials. As further application of our argument, we introduce the multivariate Al-Salam-Carlitz polynomials and establish its bilinear generating function. Other special q-series transformations are also presented.