论文标题
$ Q $ -Bernoulli jackson生成的多项式$ q $ -Bessel功能
Generalized $q$-Bernoulli polynomials generated by Jackson $q$-Bessel functions
论文作者
论文摘要
在本文中，我们介绍了由函数（包括杰克逊$ q $ -bessel functions $ j $ j^{（k）}_α（x; q）$（x; q）$（k = 1,2,3），\，\，α> -1 $ 1 $的函数生成的多项式$ b^{（k）} _ {（k）} _ {（k）} _ {（k）} _ {（k）} _ {（k）} _ {（k）} _ {（k）}（x; q）$。 $α= \ pm \ frac {1} {2} $是Bernoulli和Euler $^{，} $ s的$ q $ -sanalogs，由Ismail和Mansour介绍的$（k = 1,2）$，Mansour和Al-Towalib，for Mansour and Mansour and Mansour for Mansour and Mansour for $（k = 1,2）$（k = 1,2）$（k = 3）$。我们研究了这些多项式的主要属性，它们的大$ n $渐近学，并使用$ q $ laguerre的多项式和小$ q $ leggendre多项式提供了连接系数。
In this paper, we introduce the polynomials $B^{(k)}_{n,α}(x;q)$ generated by a function including Jackson $q$-Bessel functions $J^{(k)}_α(x;q)$ $ (k=1,2,3),\,α>-1$. The cases $α=\pm\frac{1}{2}$ are the $q$-analogs of Bernoulli and Euler$^{,}$s polynomials introduced by Ismail and Mansour for $(k=1,2)$, Mansour and Al-Towalib for $(k=3)$. We study the main properties of these polynomials, their large $n$ degree asymptotics and give their connection coefficients with the $q$-Laguerre polynomials and little $q$-Legendre polynomials.
