I've been presented with a function expansion which I'm told is correct but I can't figure out where the sign in the second term might be coming from.
$ e^{i\alpha(x_\mu + \epsilon \, n_\mu)} = e^{i\alpha(x_\mu)} ( 1 - i\,\epsilon \,n^\nu\, \partial_\nu \alpha(x_\mu) ) $
$x_\mu$, $n_\mu$ are four vectors, the metric signature is + - - - and $\epsilon$ is infinitesimal.
Taylor expanding this myself about $x_\mu$ I get
$ e^{i\alpha(x_\mu + \epsilon \, n_\mu)} = e^{i\alpha(x_\mu)} ( 1 + i\,\epsilon \,n^\nu \,\partial_\nu \alpha(x_\mu) ) $
Am I missing something or is the presented equation wrong? Perhaps to do with the metric, or maybe they are doing something other than a Taylor expansion ? :-/