Just a quick note on the wording of the Royal Resolution which mentions that Helle Thorning-Schmidt continues as prime minister (as well as a number of ministers from the three-party coalition). After discussing the matter, my best guess is that the Royal Court and the Prime Minister’s Office want to emphasise that the parliamentary basis of the two-party coalition of Social Democrats and Social Liberals has been considered.
Does this make the coalition a new government in the legal sense? Probably not, but this is a case for specialists in constitutional law and it points to the finer complications when you have a) minority governments and b) no investiture. Still, in political science and practical terms, the two-party coalition will count as a new government.