On the Generalized Newtonian Binomial Theorem

Jump To References Section

Authors

  • School of Naval Architecture & Ocean Engineering, Shanghai Jiao Tong University, Shanghai-200030 ,CN

Abstract

In this paper, a generalized binomial theorem about the real function (1+t)α (α≠ 0, 1, 2, . . . ) is proposed, which is proved to be convergent to (1 + t)α in the region -1<t<-2/â„-1(â„>0) for all real values of α(α≠0,1,2, . . .), and even in the region -2/â„-1<t<-1(â„>0) for such values of α that (1+t)α has meanings for t<-1, so that it can be convergent to (1+t)α in the whole region where (1+t)α has meanings. Moreover, the classical Newtonian binomial expression is a special case of it at â„=-1.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Published

1999-12-01

How to Cite

Liao, S.-J. (1999). On the Generalized Newtonian Binomial Theorem. The Journal of the Indian Mathematical Society, 66(1-4), 125–128. Retrieved from https://www.informaticsjournals.com/index.php/jims/article/view/21965