Mathematical Sciences: Applied Orthogonal Polynomials

本研究的主要重点将是正交多项式的数值生成，特别是其系数的计算。从这一构造性的观点出发，研究了两类新的正交多项式。其中一个涉及到一个新的权重函数，它包含一个正交多项式的平方作为因子。另一个涉及包含导数的内积。正交多项式在应用分析中是一个有用的工具：它们是逼近函数的基本元素，并用于开发复杂积分的正交格式。在这个项目中，首席研究员将研究量子化学中感兴趣的特殊正交多项式

The main focus of this research will be the numerical generation of orthogonal polynomials, specifically the computation of their coefficients. Two new classes of orthogonal polynomials are to be investigated from this constructive point of view. One involves a novel weight function that contains the square of an orthogonal polynomial as a factor. The other relates to an inner product containing derivatives. Orthogonal polynomials are a useful tool in applied analysis: they serve as basic elements for approximating functions and they are used to develop quadrature schemes for difficult integrals. In this project the principal investigator will study special orthogonal polynomials of interest in quantum chemistry.//