具有复角动量的角函数
Angular Functions with Complex Angular Momenta
摘要：
在研究多粒子过程的振幅时，以及研究涉及自旋粒子的过程的振幅时，可以使用旋转群d^ j_{μν}（z）的矩阵元。本文研究了函数d^ j_{μν}（z）对任意自变量和指数的推广.同时研究了与第二类勒让德函数类似的第二类函数。所得结果对在多粒子过程中引入复角动量起重要作用。[2013年增加：这里考虑的广义勒让德函数也可以应用于许多其他问题。
英文摘要：
In the study of the amplitudes for many-particle processes, and also for processes involving particles with spin, the use is made of matrix elements of the rotation group d^j_{μν}(z). In this paper the generalization of the functions d^j_{μν}(z) to arbitrary arguments and indices is studied. At the same time the functions of the second kind, analogous to Legendre functions of the second kind, are investigated. The results obtained play an important part in the introduction of complex angular momenta in many-particle processes. [Added in 2013: The generalized Legendre functions considered here may be applied as well to many other problems.]
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