论文标题
不确定Q积分的Lagrangian方法
A Lagrangian method for indefinite q-integrals
论文作者
论文摘要
最近引入了一种Lagrangian方法，用于得出满足同质（非均匀）二阶线性微分方程的特殊功能的不确定积分。本文将此方法扩展到包括无限期的Jackson $ Q $ - 特殊功能的综合功能，满足同质（非均匀）二阶线性$ q $ -Difference方程。使用该方法得出了许多以前已知和全新的$ q $ integrals。我们介绍了杰克逊的$ q $ - 贝塞尔功能，$ q $ - hyphemementic函数以及一些正交多项式的无限和确定$ q $ integrals的样本。
A Lagrangian method is introduced recently for deriving indefinite integrals of special functions that satisfy homogeneous (nonhomogeneous) second-order linear differential equations. This paper extends this method to include indefinite Jackson $q$-integrals of special functions satisfying homogeneous (nonhomogeneous) second-order linear $q$-difference equations. Many $q$-integrals, both previously known and completely new, are derived using the method. We introduce samples of indefinite and definite $q$-integrals for Jackson's $q$-Bessel functions, $q$-hypergeometric functions, and some orthogonal polynomials.
