What does this symbol mean in this equation?

Question

I am reading up on n-choose-k problems (Binomial Coefficients).

Wikipedia gives a multiplicative solution that is more efficient:

What symbol?

I've taken a few calculus courses, and it reminds me of how you would use the summation symbol ∑, but it also kind of looks like pi (π). What is this symbol and how can I use it to understand this formula?

Is there also a name for the symbol? I've never encountered it in all my studies (granted I'm a CS major, but we have a few math courses under our belt). — MrHappyAsthma, Sep 27 '14 at 15:49
Ah I see. I'm surprised I've never encountered a formula using this before. Now it makes much more sense! — MrHappyAsthma, Sep 27 '14 at 15:50
You may find this useful: http://en.wikipedia.org/wiki/List_of_mathematical_symbols. The symbol you are looking for is listed near the bottom of that page. — Mufasa, Sep 27 '14 at 15:50
It's the capital Greek letter, pi, for "product," the same way we use the capital Greek letter, sigma ($\Sigma$) for "sums." — Thomas Andrews, Sep 27 '14 at 15:51

score 1 · Answer 1 · answered Sep 27 '14 at 15:49

1

$\prod_{k=1}^{n} k = 1 \cdot 2 \cdot \ldots n$, i.e. a product sighn

answered Sep 27 '14 at 15:49

Alex

19,262

score 1 · Accepted Answer · answered Sep 27 '14 at 15:49

1

$\prod$ means product just as $\sum$ means sum. So, $\prod_{i=1}^5 i = 1 \cdot 2 \cdot 3 \cdot 4 \cdot 5$

Most often, it is defined as: $$ \prod_{i=0}^0 a_i = a_0 $$ $$ \prod_{i=0}^n a_i = (\prod_{i=0}^{n-1} a_i)\cdot a_n$$

answered Sep 27 '14 at 15:49

Krijn

1,945
16
32

score 1 · Answer 3 · answered Sep 27 '14 at 15:52

1

Pi as in product:

$\prod_{k=1}^n a_k=a_1\cdot a_2\cdots a_{n-1}\cdot a_n$.

answered Sep 27 '14 at 15:52

Yiorgos S. Smyrlis

83,933

$k=1$, you meant? You have $k-1$ – Thomas Andrews Sep 27 '14 at 15:54
Corrected it. Thanks. – Yiorgos S. Smyrlis Sep 27 '14 at 15:56

What does this symbol mean in this equation?

3 Answers3