Tigers make a variety of sounds. They include a number of roars and growls, the loudest of those being most likely the full-throated aaonh, usually made during the mating season by males and aestrous females. ... Tigers go woof when they are caught unawares, a short, sharp detonation of fury that would instantly make your legs jump up and run away if they weren't frozen to the spot. ... Tigers make other sounds too. They grunt and moan. They purr, though not as melodiously or frequently as small cats, and only as they breathe out. ...Tigers even go meow, with an inflection similar to that of domestic cats, but louder and deeper in range, not as encouraging to one to bend down and pick them up. ...

I had heard all of these sounds growing up. Except for prusten. ... Prusten is the quietest of tiger calls, a puff through the nose to express friendliness and harmless intentions.

Richard Parker did it again, this time with a rolling of the head. He looked at me exactly as if he were asking me a question.1

When tigers seem to agree with each other, they make a soft sound often called "prusten" by handlers (or "chuffing" by biologists). It is a low-frequency noise created by exhaling through the nostrils, and sounds somewhat like a human exhaling strongly while letting the lips flap loosely or, more correctly, by forming the "f" sound with the lips and exhaling while vibrating the tongue against the roof of the mouth (sort of like a rolled F). In the wild, it is often heard between mothers and cubs, or between a mating pair, and in captivity the noise is directed towards familiar zookeepers with whose presence the tiger has gotten comfortable.

I'm told that prusten is a German word meaning "to sneeze or snort" or "to suddenly burst into laughter" (the form losprusten is used in this case, thanks Siobhan), but I can't find it in any dictionary — the closest I can find is "pusten," meaning "to blow" or "to pant." The Big Bad Wolf's line in the story of the Three Little Pigs is lch werde strampeln und trampeln, ich werde husten und prusten ("I'll pedal and trample, I'll cough and blow"), and I saw it once used to describe the chugging noise that a train engine makes.

1: Yann Martel, Life of Pi, Harcourt, Inc., New York: 2001. Pp. 163–164.
I suggest that everyone who's ever liked tigers read this book now.