We obtain a class of exact solutions for a Bessel-type differential equation, which is a five-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 a quasirational Laguerre function (Laguerre polynomials in the reciprocal argument). The expansion coefficients of the series are orthogonal polynomials in the equation parameters space.

中文翻译：

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使用三对角表示法求解贝塞尔型微分方程

我们获得了 Bessel 型微分方程 的一类精确解，它是一个在原点具有不规则（本质）奇点的二阶五参数线性常微分方程。解是使用三对角表示法 (TRA) 作为根据拟有理拉盖尔函数（倒数参数中的拉盖尔多项式）编写的平方可积函数的有界系列获得的。级数的展开系数是方程参数空间中的正交多项式。