How to expand function cos(y+ilogx)\cos(y+i\log{x}) in powers of xx?

I have the following, probably very simple question.
How can I get Mathematica\it{Mathematica} to power expand function cos(y+ilog(x))\cos(y+i \log(x)) in powers of xx? This function obeys a well defined Laurent expansion about x=0x=0 and I would like Mathematica\it{Mathematica} to give 1xeiy/2+xe−iy/2\frac1{x}e^{i y}/2+x e^{-iy}/2 upon evaluation of

Series[Cos[y + I Log[x]], {x, 0, 1}]

However, the result is

Cos[y + I Log[x]]

i.e. the original expression. I can bet that in some circumstances such expansion worked without any effort from my side.

I wonder what is the right way to obtain the expansion of the function cos(y+ilog(x))\cos(y+i \log(x)) in powers of xx.

Any help is appreciated.



1 Answer


One way to get the desired output is to use TrigToExp

TrigToExp[Cos[y + I Log[x]]]
(* E^(I y)/(2 x) + 1/2 E^(-I y) x *)



This indeed works, thank you.
– Weather Report
May 8 ’14 at 17:25