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<p>We introduce the notions of (<i>p</i>, <i>q</i>)-differential for complex discrete functions and (<i>p</i>, <i>q</i>)-complex differential operators in a sense of Pashaev. The (<i>p</i>, <i>q</i>)-analog of the <i>q</i>-binomial formula is presented and the (<i>p</i>, <i>q</i>)-Taylor expansion is constructed for (<i>p</i>, <i>q</i>)-analytic functions. These results provide a generalized framework for (<i>p</i>, <i>q</i>)-calculus, contributing to its applications in mathematical analysis and related fields.</p>

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(p, q)-Analytic Functions and a Complex (p, q)-Binomial Formula

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • İlker Gençtürk

摘要

We introduce the notions of (p, q)-differential for complex discrete functions and (p, q)-complex differential operators in a sense of Pashaev. The (p, q)-analog of the q-binomial formula is presented and the (p, q)-Taylor expansion is constructed for (p, q)-analytic functions. These results provide a generalized framework for (p, q)-calculus, contributing to its applications in mathematical analysis and related fields.