Brian Steinberg Senior TV EditorThe Murdochs, the media-mogul family that controls Fox News Channel, are about to be the subject of a new documentary series that will be distributed by one of their main rivals.CNN expects to launch a six-part documentary series, “The Murdochs: Empire of Influence,” on CNN Plus, the streaming video site slated to launch in weeks to come. The series is produced with The New York Times and Left/Right and is based on the New York Times Magazine article “How Rupert Murdoch’s Empire of Influence Remade the World,” by journalists Jonathan Mahler and Jim Rutenberg.