Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I wonder if there exists a formula for this function? $$f(x) = (x-1)(x-2)(x-3) \cdots (x-k)$$ I want to know the coefficient of each $x^i$, and the first thing I came up with was to find the expansion of this expression. Any idea?

Thanks,

share|improve this question
    
I'm guessing that the $k$ in the formula for $f$ is not the same as the $k$ in "I want to know the coefficient of each $x^k$", so I suggest you change the latter to "of each $x^i$" to avoid confusion. –  Arturo Magidin Apr 15 '11 at 17:23
    
@Arturo Magidin: You're just so right ^_^! Thank you. –  Chan Apr 15 '11 at 17:23

1 Answer 1

up vote 11 down vote accepted

Look up the Stirling numbers and the falling factorial.

share|improve this answer
1  
Alternatively, one can use Pochhammer symbols to represent these entities. –  J. M. Apr 16 '11 at 18:03

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.