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<p>In this paper, we define an extended <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( \textit{q} \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="italic">q</mi> </math></EquationSource> </InlineEquation>-Jacobi polynomial using the Wright-type <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\( \textit{q} \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="italic">q</mi> </math></EquationSource> </InlineEquation>-hypergeometric function and discuss its analytical properties, including recurrence and contiguous relations, integral and derivative formulas, as well as integral representations. Also, integral transforms, such as the Laplace, Sumudu, and Natural transforms have been derived.</p>

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Extended q-Jacobi polynomial and its properties

  • 期刊论文

  • 发表日期：

    2026年6月20日

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  • S. B. Gajera,
  • R. K. Jana,
  • N. A. Khan,
  • A. K. Shukla

摘要

In this paper, we define an extended \( \textit{q} \) q -Jacobi polynomial using the Wright-type \( \textit{q} \) q -hypergeometric function and discuss its analytical properties, including recurrence and contiguous relations, integral and derivative formulas, as well as integral representations. Also, integral transforms, such as the Laplace, Sumudu, and Natural transforms have been derived.