Mathematical Sciences: Applied Orthogonal Polynomials

这项研究的主要重点将是数字 正交多项式的生成，特别是 计算其系数。 两类新的正交 多项式是从这个建设性的点进行研究 的观点。 一个涉及一个新的权重函数，其中包含 正交多项式的平方作为因子。 另 涉及一种含有导数的内积。 正交 多项式是应用分析中的有用工具：它们用作 近似函数的基本元素，它们用于 为困难的积分开发求积方案。 在这 项目主要研究者将研究特殊的正交 量子化学中的多项式。

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.//