Tagged Questions
4
votes
4answers
83 views
Big Greeks and commutation
Does a sum or product symbol, $\Sigma$ or $\Pi$, imply an ordering?
Clearly if $\mathbf{x}_i$ is a matrix then:
$$\prod_{i=0}^{n} \mathbf{x}_i$$
depends on the order of the multiplication. But, ...
3
votes
2answers
36 views
Summation and Product Bounds
If I have a sum or product whose upper index is less than its start index, how is this interpreted? For example:
$$\sum_{k=2}^0a_k,\qquad \prod_{k=3}^1b_k$$
I want to say that they are equal to the ...
2
votes
0answers
50 views
“Product” bundle notation.
Let $\newcommand{\Spin}{\operatorname{Spin}}M$ and $M'$ be two manifolds, equipped with a principal $\Spin_n$ and $\Spin_{n'}$ bundle called $P$ and $P'$, respectively.
Then there is an induced ...
-2
votes
4answers
94 views
Derivative of product notation?
Presume $f(x,y)$ is a continuous function. How would I take the derivative of $$\prod_{x=1}^N f(x,y)$$?
Edit: derivative with respect to $x$, that is.
2
votes
1answer
71 views
Limit of an n-ary product
Since a definite integral is defined as
$$\lim_{n\to\infty} \sum_{i=0}^n f(x_i^*)\,\Delta x = \int_a^b f(x)\,dx$$
and the integral is much easier to calcluate than a sum, if we change the sum to a ...
4
votes
1answer
114 views
Operators - sums, products, exponents, etc.
$(x + x + \cdots + x)$, where $x$ added $n$ times can be written as $x * n$.
$(x * x * \cdots * x)$, where $x$ multiplied $n$ times can be written as $x ^ n$.
Is there an operator, such that if ...
3
votes
2answers
55 views
interval for a product to infinity
I was wondering - how would I specify the interval (the amount that n increases each time) between terms? Is that possible? What if I want it to increase by, say, ...
