Taylor series of i[x]

[sheldonison]

I have been interested in that what the taylor series of i[x] is for long years.
There are infinity base units from i[0]=1 through i[pi] to i[10000...]. Their multiplication with each other usually is -1, but we can be sure only when x is an integer bigger than 0.
Here is a multiplication table for base units from i[0] to i[15]: https://en.wikipedia.org/wiki/Sedenion
(So we xor their indexes: n^m where ^ is the xor binary operator giving somehow a sign ... unfortunately I do not know what the form for this is.)
But the biggest question is that how we can get its taylor series. Any idea?

I'm not familiar with Sedenion, but it is an abstract algebra concept, not a complex analytic function, right?  So by definition, unless there is some mapping to a complex function, then it would not have a Taylor series...