I've seen this a couple times. What does the part where y is over k with a space between them? What does this imply? (Below is the Binomial Theorem equation)
$(x + a)^y = \sum\limits_{k=1}^{\infty}\binom{y}{k}x^ka^{y-k}$
I've seen this a couple times. What does the part where y is over k with a space between them? What does this imply? (Below is the Binomial Theorem equation)
$(x + a)^y = \sum\limits_{k=1}^{\infty}\binom{y}{k}x^ka^{y-k}$
It is a binomial coefficient. The symbol is typically defined by $\binom{n}{k}=\frac{n!}{(n-k)!\times k!}$ where $n$ and $k$ are non-negative integers, and the exclamation point $!$ denotes the factorial.
However, in the example you cite, which is often called the generalized binomial theorem, in place of the integer $n$ we can actually use any real number $\nu$ (this is the Greek letter nu), and we define $\binom{\nu}{k}=\frac{\nu\times(\nu-1)\times\cdots\times(\nu-k+1)}{k!}$ This agrees with the standard definition when $\nu$ is a non-negative integer.
For an example of how this symbol is computed, $\binom{5}{2}=\frac{5!}{3!\times 2!}=\frac{5\times 4\times 3\times 2\times 1}{(3\times 2\times 1)\times(2\times 1)}=\frac{120}{12}=10$
Many texts in probability theory sometimes write the binomial coefficient $\binom{n}{k}$ as ${}_nC_k$, where it is called "$n$ choose $k$."