论文标题
使用$ q $ -RICATTI方程的方法不确定$ q $ intergalls
Indefinite $q$-integrals from a method using $q$-Ricatti equations
论文作者
论文摘要
较早的工作引入了一种从二阶线性$ q $ -Difference方程中获取无限$ q $ integrals的无限$ q $ integrals的方法。在本文中，我们根据非线性和一阶的$ q $ -riccati方程式对方法进行了重新制定。我们使用这些riccati方程的片段得出$ q $ integrals，在这里仅详细检查了两种特定的片段类型。 The results presented here are for $q$-Airy function, Ramanujan function, Jackson $q$-Bessel functions, discrete $q$-Hermite polynomials, $q$-Laguerre polynomials, Stieltjes-Wigert polynomial, little $q$-Legendre, and big $q$-Legendre polynomials.
Earlier work introduced a method for obtaining indefinite $q$-integrals of $q$-special functions from the second-order linear $q$-difference equations that define them. In this paper, we reformulate the method in terms of $q$-Riccati equations, which are nonlinear and first order. We derive $q$-integrals using fragments of these Riccati equations, and here only two specific fragment types are examined in detail. The results presented here are for $q$-Airy function, Ramanujan function, Jackson $q$-Bessel functions, discrete $q$-Hermite polynomials, $q$-Laguerre polynomials, Stieltjes-Wigert polynomial, little $q$-Legendre, and big $q$-Legendre polynomials.
