论文标题
非常特殊的功能：离散变量的Chebyshev多项式及其物理应用
Very special special functions: Chebyshev polynomials of a discrete variable and their physical applications
论文作者
论文摘要
在将近六十年的时间里，离散实际变量的Chebyshev多项式在旋转物理学，自旋断层扫描，操作员扩展的开发以及定义张量操作员当量中的应用中发现了应用。详细讨论了这些多项式的特性，然后提供了示例以说明其在磁共振中的应用的多样性。这些示例包括使用Chebyshev多项式操作员用作扩展旋转操作员，投影操作员和Stratonovich-Weyl操作员的正顺序基础。指出和利用了离散真实变量的Chebyshev多项式的双重性，并且可以被发现和利用，并且表明可以将Chebyshev多项式操作员重新耦合为rank-Zero复合张量由旋转和空间孔的乘积定义。这些应用示例表明，离散实际变量的Chebyshev多项式是旋转物理学，特殊功能，角动量（RE）耦合和旋转组不可减至表示的独特联系。
Over nearly six decades, the Chebyshev polynomials of a discrete real variable have found applications in spin physics, spin tomography, in the development of operator expansions, and in defining tensor operator equivalents. The properties of these polynomials are discussed in detail, and then examples are provided to illustrate the diversity of their applications in magnetic resonance. These examples include the use of the Chebyshev polynomial operators as an orthonormal basis to expand rotation operators, projection operators, and the Stratonovich-Weyl operator. The duality of the Chebyshev polynomials of a discrete real variable as Clebsch-Gordan coupling coefficients is noted and exploited, and it is shown that the Chebyshev polynomial operators can be recoupled as a rank-zero composite tensor defined by the product of a spin and spatial tensor. These application examples demonstrate that the Chebyshev polynomials of a discrete real variable are a unique nexus for spin physics, special functions, angular momentum (re)coupling, and irreducible representations of the rotation group.
