Barrons AP Calculus - David Bock

Then

COMMON MACLAURIN SERIES

We list here for reference some frequently used Maclaurin series expansions together with their
intervals of convergence:

FUNCTIONS THAT GENERATE NO SERIES.

Note that the following functions are among those that fail to generate a specific series in (x − a)
because the function and/or one or more derivatives do not exist at x = a: