论文标题
贝塞尔型微分方程的系列解决方案在正交多项式和物理应用方面
Series solutions of Bessel-type differential equation in terms of orthogonal polynomials and physical applications
论文作者
论文摘要
我们获得了贝塞尔型微分方程的一类精确解，该方程是六参数线性的二阶线性微分方程，其原点上具有不规则（必需的）奇异性。使用Tridia -Gonal表示方法（TRA）作为有限的平方集成函数来获得解决方案，该函数根据实际线上的Bessel多项式编写。该系列的扩展系数是方程参数空间中的正交多项式。我们使用我们的发现来获得Schrödinger方程的解决方案，以获得一些新的潜在功能。
We obtain a class of exact solutions of a Bessel-type differential equation, which is a six-parameter linear ordinary differential equation of the second order with irregular (essential) singularity at the origin. The solutions are obtained using the Tridiagonal Representation Approach (TRA) as bounded series of square integrable functions written in terms of the Bessel polynomial on the real line. The expansion coefficients of the series are orthogonal polynomials in the equation parameters space. We use our findings to obtain solutions of the Schrödinger equation for some novel potential functions.
