q-Difference equations for the generalized Cigler’s polynomials
q-Difference equations for the generalized Cigler’s polynomials
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DOI：
10.1080/10236198.2017.1422247
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发表时间：
2018-01
影响因子：
1.1
通讯作者：
Xue-Fang Wang;Jianbing Cao
中科院分区：
文献类型：
--
作者：
Xue-Fang Wang;Jianbing Cao
本文用齐次q-差分方程的方法证明了几类四元多项式的母函数。我们利用Liu的[Ramanujan Math.Soc.20（2013），pp. 213-250。]和Fang的[应用数学计算. 248（2014），pp. 550-561.]继续研究Moncler的结果[J. Differ.当量ag Appl. 22（2016），pp. 1880-1892年。此外，我们推导出了型生成函数的Spirtler多项式。此外，还建立了变换公式与齐次q-差分方程之间的关系。作为应用，我们得到了多线性和多母函数。最后，利用齐次q-差分方程的方法推广了Andrews-Askey积分、矩积分和Askey-Roy积分。
Abstract In this paper, we show how to prove several types of generating functions for Cigler’s polynomials involving four variables by the method of homogeneous q-difference equations. We utilize some methods and results of Liu’s [Ramanujan Math. Soc. 20 (2013), pp. 213–250.] and Fang’s [Appl. Math. Comput. 248 (2014), pp. 550–561.] continue to study Cigler’s results [J. Differ. Equ. Appl. 22 (2016), pp. 1880–1892.]. In addition, we deduce type generation functions for Cigler’s polynomials. More over, we build relations between transformation formulas and homogeneous q-difference equations. And then, we gain multilinear and multiple generating functions for Cigler’s polynomials as application. Finally, we generalize Andrews–Askey integrals, moment integrals and Askey–Roy integrals by the method of homogeneous q-difference equations.