A new formula is derived that generalizes an earlier result for the infinite integral over three spherical Bessel functions. The analytical result involves a finite sum over associated Legendre functions, P_l~m(x) of degree l and order m. The sum allows for the values of |m| that are greater than l. A generalization for the associated Legendre functions to allow for any rational m for a specific l is also shown.
展开▼
机译：导出了一个新公式，该公式将三个球贝塞尔函数上的无穷积分的较早结果推广为广义。分析结果涉及相关的勒让德函数，阶数为m的P_1〜m（x）的有限和。总和允许| m |的值大于l。还显示了关联的Legendre函数的一般化，以允许特定l的任何有理m。
展开▼
