区间上正交多项式熵的计算
Computation of the entropy of polynomials orthogonal on an interval
AI总结：
提出一种仅利用多项式递推系数计算区间正交多项式熵的有效方法，并应用于Gegenbauer多项式和球谐函数的熵计算。
摘要：
我们给出了一种有效的方法来计算实轴区间上正交多项式的熵，该方法仅需输入这些多项式满足的递推关系的系数。该算法基于与多项式自然相关的两个概率测度的互能的级数表达式。详细分析了Gegenbauer多项式的特例。这些结果也应用于球谐函数熵的计算，这对于研究熵不确定关系以及中心势场中物理系统的空间复杂性很重要。
英文摘要：
We give an effective method to compute the entropy for polynomials orthogonal on a segment of the real axis that uses as input data only the coefficients of the recurrence relation satisfied by these polynomials. This algorithm is based on a series expression for the mutual energy of two probability measures naturally connected with the polynomials. The particular case of Gegenbauer polynomials is analyzed in detail. These results are applied also to the computation of the entropy of spherical harmonics, important for the study of the entropic uncertainty relations as well as the spatial complexity of physical systems in central potentials.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
