中文摘要：

广义Stirling数都是由2类函数相互表达定义的,在第一类q-Legendre-Stirling数的基础上,提出第二类q-Legendre-Stirling数概念.研究了第二类q-Legendre-Stirling数的递推关系、生成函数,及相关的组合恒等式,并且给出了2类q-Legendre-Stirling数之间的关系.

英文摘要：

The generalized Stifling numbers are defined by two kinds of functions each other, based on the definition of the q - Legendre-Stirling numbers of the first kind, the concept ofq - Legendre-Stirling numbers of the second kind is proposed. The recurrence relations ofq - Legendre-Stifling numbers of the second kind, generating function and some related combinatorial identities are studied. In addition the relationships between two kinds ofq - Legendre- Stifling numbers are given.