论文标题
$ Q $ -Lidstone系列涉及$ Q $ -Bernoulli和$ Q $ -Euler polyenmials由第三个Jackson $ Q $ -Bessel函数
The $q$-Lidstone series involving $q$-Bernoulli and $q$-Euler polynomials generated by the third Jackson $q$-Bessel function
论文作者
论文摘要
n本文，我们提出了$ q $ -bernoulli和$ Q $ -Euler polyenerials由第三杰克逊$ Q $ -Bessel函数生成的$ Q $ -Bessel函数，以构建新型的$ Q $ lidstone扩展定理。我们证明，可以通过$ q $ lidstone多项式扩展整个功能，即$ q $ -Bernoulli多项式，系数是$ Q $ \ frac {δ_Qf（z）} {z q $ q $ q $ \ frac的均匀功能。另一种表单基于$ q $ - 欧拉特尔多项式，以$ q $ lidstone的多项式扩展了功能，并且系数包含$ q $ - 衍生的$ \ frac {Δ_Qf（z）} {Δ_QZ} $的均匀和奇数。
n this paper, we present $q$-Bernoulli and $q$-Euler polynomials generated by the third Jackson $q$-Bessel function to construct new types of $q$-Lidstone expansion theorem. We prove that the entire function may be expanded in terms of $q$-Lidstone polynomials which are $q$-Bernoulli polynomials and the coefficients are the even powers of the $q$-derivative $\frac{δ_q f(z)}{δ_q z}$ at $0$ and $1$. The other forms expand the function in $q$-Lidstone polynomials based on $q$-Euler polynomials and the coefficients contain the even and odd powers of the $q$-derivative $\frac{δ_q f(z)}{δ_q z}$.
