关于 q 指数方程展开式和 q-Hardy-Hille 型公式的说明

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED

Bulletin des Sciences Mathematiques Pub Date : 2024-08-09 DOI:10.1016/j.bulsci.2024.103489

Jian Cao , Qi Bao , Sama Arjika

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引用次数: 0

摘要

利用二项式定理的非交换q解析式，我们为q-拉盖尔多项式构造了新的q-指数算子，并推导出q-指数方程的展开式，从而用系统的方法研究涉及q-拉盖尔多项式的求和与积分，如罗杰斯公式、哈代-希尔公式、混合型、U(n+1)型q-拉盖尔多项式的生成函数和变换同一性。我们概括了 [Sci.

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A note on expansions of q-exponential equations and q-Hardy–Hille type formulas

By using noncommutative q-analogue of binomial theorem, we construct new q-exponential operators for q-Laguerre polynomials and deduce expansions of q-exponential equations, which lead us to use a systematic method for studying summations and integrals involving q-Laguerre polynomials, such as the Rogers formula, Hardy–Hille formula, mixed-type, $U (n + 1)$ type generating functions for q-Laguerre polynomials and transformational identity. We generalize some results of [Sci. China Math. 66(2023), 1199–1216] and [Adv. Math. 131(1997), 93–187].