安裝中文字典英文字典辭典工具!
安裝中文字典英文字典辭典工具!
|
- What does the $\prod$ symbol mean? - Mathematics Stack Exchange
21 The symbol $\Pi$ is the pi-product It is like the summation symbol $\sum$ but rather than addition its operation is multiplication For example, $$ \prod_ {i=1}^5i=1\cdot2\cdot3\cdot4\cdot5=120 $$ The other symbol is the coproduct
- meaning - What does prod issues mean in computer science and software . . .
DevOps engineers are those who are good at debugging, troubleshooting, analyzing prod issues and providing solutions Who have good hands on technologies like unix shell scripting, perl, SQL etc
- real analysis - Finding Value of the Infinite Product $\prod \Bigl (1 . . .
Here is a hint to evaluate $$\prod_ {n=2}^\infty\left (1-\frac1 {n^2}\right) :$$ Note that this is a telescoping product, since $1-1 n^2= (n-1) (n+1) n^2$ Now play with the first few terms to see the emerging pattern
- How do I take the natural log of the product $L (\theta) = \prod _ {i=1 . . .
I'm trying to take the natural log, $\ln (L (\theta))$, but I'm not sure how this works with respect to $\prod$ Does anyone know what the process for this log is?
- General formula for calculating $\\prod_i^n (1+a_i)$
$$\displaystyle\prod\limits_ {i=1}^ {n} \left (1+a_i\right) \,\, = \,\, \displaystyle\sum_ {S \,\subseteq \, \ {1,\, 2,\, 3,\, \dots\,,\, n\}} \,\,\,\left (\,\prod
- Is $\mathop {\Large\times}$ (\varprod) the same as $\prod$?
At first I thought this was the same as taking a Cartesian product, but he used the usual $\prod$ symbol for that further down the page, so I am inclined to believe there is some difference Does anyone know what it is? This old SE question shows the symbol I am referring to, but sadly does not provide an explanation
- Proving a result in infinite products: $\prod (1+a_n)$ converges (to a . . .
Questions But from here I don't know if I am right, how to conclude and solve the converse part to say that we have a non zero limit, and another thing Can someone provide explicit examples of a sequence of complex numbers $\ {a_n\}$ such that $\sum a_n$ converges but $\prod (1+a_n)$ diverges and the other way around (This is $\prod (1+a_n)$ converges but $\sum a_n$ diverges )? Thanks a lot in
- If $\sum a_n^k$ converges for all $k \geq 1$, does $\prod (1 + a_n . . .
By definition, an infinite product $\\prod (1 + a_n)$ converges iff the sum $\\sum \\log(1 + a_n)$ converges, enabling us to use various convergence tests for infinite sums, and the Taylor expansion $
|
|
|