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Suppose you have an exception object acquired from somewhere. The exception is no longer active on the stack. Now you want to format the exception like format_exception would (to log it, perhaps). To do this you apparently need to call:
 format_exception(type(exc), exc, exc.__traceback__)
This seems redundant, so it would be nice to have a simpler call. Too bad the name format_exception is already taken. But, leaving that aside, the above is not documented in the traceback module. The last example shows the (type(exc), exc) call form for format_exception_only, but that's as close as it gets.

Why not reuse format_exception(exc)?
in 2.7 you could write "raise type, value, traceback", or "raise value".
I suggest that traceback.format_exception take the same route, and accept both (type, value, traceback) and (value).

Sounds OK to me, though I am worried others will think that kind of variable signature (where the type of the first argument depends on the number of arguments passed) is bad.

As of 3.5 there is this option:
traceback.TracebackException.from_exception(exc).format()
Perhaps that can be mentioned in the doc for traceback.format_exception().

In issue 26389 the api was changed so that now format_exception(exc) works.