Presented in this paper is a convergence theorem for a kind of composite power series expansions whose coefficients can be expressed by using Faa` di Bruno’s formula. A related problem is proposed as a remark, and a ...Presented in this paper is a convergence theorem for a kind of composite power series expansions whose coefficients can be expressed by using Faa` di Bruno’s formula. A related problem is proposed as a remark, and a few examples are given as applications.展开更多
It is shown that Howard＇s degenerate weighted Stirling numbers can be used to construct a fruitful summation formula for a class of formal power series involving generalized factorials.This is achieved with the aid o...It is shown that Howard＇s degenerate weighted Stirling numbers can be used to construct a fruitful summation formula for a class of formal power series involving generalized factorials.This is achieved with the aid of a series-transformation formula due to He,Hsu and Shiue,and several identities involving generalized Stirling numbers and Bell numbers are given to illustrate the application of the formula obtained.展开更多
文摘Presented in this paper is a convergence theorem for a kind of composite power series expansions whose coefficients can be expressed by using Faa` di Bruno’s formula. A related problem is proposed as a remark, and a few examples are given as applications.
文摘It is shown that Howard＇s degenerate weighted Stirling numbers can be used to construct a fruitful summation formula for a class of formal power series involving generalized factorials.This is achieved with the aid of a series-transformation formula due to He,Hsu and Shiue,and several identities involving generalized Stirling numbers and Bell numbers are given to illustrate the application of the formula obtained.
