环势及一类涉及复杂变元的泛关联勒让德多项式的积分
Ring-shaped potential and a class of relevant integrals involved universal associated Legendre polynomials with complicated arguments
摘要：
我们发现极角微分方程的解可以写成普适的相关勒让德多项式。利用它的母函数得到了一类有趣的复宗量积分的解析结果。本方法原则上可推广到其它特殊函数的积分。作为例子，我们还研究了一个典型的贝塞尔积分与复杂的论点。
英文摘要：
We find that the solution of the polar angular differential equation can be written as the universal associated Legendre polynomials. Its generating function is applied to obtain an analytical result for a class of interesting integrals involving complicated argument. The present method can in principle be generalizable to the integrals involving other special functions. As an illustration we also study a typical Bessel integral with a complicated argument.
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