论文标题
一些涉及正常排序产生的退化stirl数字的身份
Some identities involving degenerate Stirling numbers arising from normal ordering
论文作者
论文摘要
在本文中，我们得出了第一类的退化stirling数字的一些身份和复发关系，这些数字是第一类和第二类的普通stirling数字的退化版本。它们是从数量运算符及其反转，玻色子操作员的某些关系以及Stirling数字本身的复发关系的正常积分功能中推导的。在这里，我们注意到，虽然数字运算符的积分功率的正常顺序借助第二类的stirling数字来表示，但数字运算符的退化积分幂的代表是通过第二类的退化stirling数来表示。
In this paper, we derive some identities and recurrence relations for the degenerate Stirling numbers of the first kind and of the second kind which are degenerate versions of the ordinary Stirling numbers of the first kind and of the second kind. They are deduced from the normal oderings of degenerate integral powers of the number operator and their inversions, certain relations of boson operators and from the recurrence relations of the Stirling numbers themselves. Here we note that, while the normal ordering of an integral power of the number operator is expressed with the help of the Stirling numbers of the second kind, that of a degenerate integral power of the number operator is represented by means of the degenerate Stirling numbers of the second kind.
