Yu Yi-Kuo
National Center for Biotechnology Information, National Library of Medicine, National Institutes of Health, Bethesda, MD 20894, USA.
Physica A. 2003 Aug 15;326(3-4):522-33. doi: 10.1016/s0378-4371(03)00335-2.
The exact analytical result for a class of integrals involving (associated) Legendre polynomials of complicated argument is presented. The method employed can in principle be generalized to integrals involving other special functions. This class of integrals also proves useful in the electrostatic problems in which dielectric spheres are involved, which is of importance in modeling the dynamics of biological macromolecules. In fact, with this solution, a more robust foundation is laid for the Generalized Born method in modeling the dynamics of biomolecules.
给出了一类涉及复杂自变量（连带）勒让德多项式的积分的精确解析结果。所采用的方法原则上可以推广到涉及其他特殊函数的积分。这类积分在涉及电介质球体的静电问题中也证明是有用的，这在对生物大分子动力学进行建模时很重要。事实上，有了这个解，为广义玻恩方法在生物分子动力学建模中奠定了更坚实的基础。
