Posts Tagged ‘factorial’

Speaking of the Gamma Function…

October 8, 2010

Yesterday I gave a talk to the University of Michigan undergraduate Math Club on extensions and generalizations of the factorial function.  (I talked about in what senses the gamma function is and is not unique as an extension of n!, mentioned the Hadamard gamma and other entire extensions, and for dessert defined Bhargava’s factorials.)  In that talk I told an anecdote (true story, and the “I” of the story really is me) which I actually hadn’t been planning to tell; it just came out.  But the laughter was so great that I thought I’d post it here also.

Speaking of the gamma function, I was teaching a probability class, and it so happened that integrals of the form \int_0^\infty t^{z-1}e^{-t}\/dz came up frequently in the examples and homework.  I overheard two of my students remarking on this phenomenon before class.

“I’ve noticed that integrals like that always come out to factorials,” said the first guy, “1, 2, 6, and so on.”

So now he has my undivided attention.  This kid wasn’t even a math major, and he picked up on the pattern.  He’s clearly not done talking, and I want to know what his next piece of insight is going to be.

“It’s kinda useful,” he went on, “because when I need to figure out a big factorial I don’t know, like 19! or something, I can just write down the integral and do it on my calculator.”

To this day, I consider it one of my greatest accomplishments as an educator that I did not laugh nor spray the coffee I was drinking out my nose.

“Why don’t you just use the factorial button?” asked his friend.

“There’s a factorial button?”


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