Series that Begin with (a+b*i)^n - MathOverflow [closed]most recent 30 from http://mathoverflow.net2013-05-24T10:15:28Zhttp://mathoverflow.net/feeds/question/61774http://www.creativecommons.org/licenses/by-nc/2.5/rdfhttp://mathoverflow.net/questions/61774/series-that-begin-with-abinSeries that Begin with (a+b*i)^nMarvin Ray Burns2011-04-15T01:51:44Z2011-04-15T01:51:44Z
<p>Since -1 = i^2 I thought that there could be some meaning behind alternating series that instead of begining with (-1)^n begin with (a+b*i)^n for a and b != 0; does anyone know where I can find out more about such a series?
As an example,<BR>$\sum _{n=0}^{\infty } \frac{(a+i b)^n}{n!}=e^{a+i b}$ </p>