On Taylor series expansion of $(1+ z)^{A}$ for $|z|>1$

Abstract

It is well known that the Taylor series expansion of $(1+ z)^{A}$ does not converge for $|z|>1$ where A is a real number which is not equal to zero or a positive integer. A limited series expansion of this expression is obtained in this paper for $|z|>1$ as a product of convergent series.