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Questions tagged [products]

Questions about the use of `Product`, `NProduct`, and other types of multiplication, like `Dot`.

1 vote
1 answer
155 views

Suppose we have the following function, where $s\in\mathbb{R}$ and $t_1,t_2,n\in\mathbb{N}\cup\{0\}$ are constants: $$\mathbf{P}(r)=\left(t_1+\prod_{k=1}^{r}(t_2+k^{s})\right)^n$$ Question: What is ...
Arbuja's user avatar
  • 51
0 votes
0 answers
159 views

I'm still trying to learn how to code the results of the LHS and RHS of this famous equation into a table: $$\sum_{n=1}^\infty \frac1n=\prod_{i=1}^\infty\frac{1}{1-\frac{1}{p_i}}\tag{A}$$ I asked this ...
user475550's user avatar
6 votes
1 answer
463 views

It's my understanding that if I take $\vec{x}=\begin{pmatrix} 1\\ 0 \end{pmatrix}$ and then do $\vec{x}\otimes\vec{x}$ I should be getting$\begin{pmatrix} 1\\ 0\\ 0\\0 \end{pmatrix}$ but when I run <...
Daniel's user avatar
  • 470
6 votes
3 answers
474 views

EDITED QUESTION: I edit my question to be as clear as possible, as I find the problem quite confusing and severe, and the previous answers unfortunately not helpful. I define two arrays of matrices ...
Philipp Strasberg's user avatar
1 vote
1 answer
141 views

I have a polynomial in say a,b, and c, and I want this to be in terms of x,y, and z where a^(i_)*b^(j_)*c^(k_) ->x^(i+j+k+1)*y^(i+k+1)*z^(k+1), but if I try to ...
Matthew Crawford's user avatar
1 vote
1 answer
202 views

In the following code, I have two pairs of vector u0,u1 and v0,...
phy_std's user avatar
  • 322
1 vote
1 answer
143 views

I want to be able to simplify expressions of vectors, such as: Cross[Cross[x,p],Cross[Cross[y,q],Cross[x,p]]] I know I could create my own rule sets, however I'd ...
ions me's user avatar
  • 1,145
2 votes
2 answers
114 views

I have tried all the way but I could not find a code for that line. It is consisting of three conditions.
Nithiya V 22PHD1215's user avatar
2 votes
3 answers
177 views

How to verify that FactorialPower[x, m*n, k] is always the same as Product[FactorialPower[x - i*k, n, m*k], {i, 0, m - 1}] ...
PalmTopTigerMO's user avatar
6 votes
3 answers
511 views

I have two expressions with the Gamma function that are identical: ...
Vaclav Kotesovec's user avatar
6 votes
2 answers
235 views

Pattern recognition doesn't work as I would expect when trying to match products, for example Cases[a[1] b[1] a[2] b[2], x___ a[k_] b[k_] -> k, All] {1} ...
Adrien Martina's user avatar
2 votes
0 answers
85 views

TLDR: How to expand gamma functions or Pochammer symbols in an arbitrarily long product? Some context I am trying to find out a closed-form expression for $\langle r^\alpha\rangle$ for the non-...
Sanjana's user avatar
  • 195
2 votes
3 answers
437 views

I want to simplify expressions containing DiracDelta products. For example I want to simplify the expression $$\delta(z-2)\delta(k-5)\delta(t-z-k-9)$$ to give the answer $$\delta(z-2)\delta(k-5)\delta(...
Mohamed Mostafa's user avatar
1 vote
0 answers
88 views

I am trying to plot the $|f(\theta,\phi)|^2$, where the expression of $f(\theta,\phi)$ is as under: $$ f =\sum_{n_j}\Pi_{j_x,j_y,j_z}P_{n_j}\sum_{l}A_s \text{e}^{-ia(l_1q_x+l_2q_y+l_3q_z)}\times \...
R. Bhattacharya's user avatar
1 vote
0 answers
164 views

EDIT: see here I am new to Mathematica and I am trying to work though deriving the maximum likelihood estimator for the Poisson distribution as an exercise to familiarize myself with how Mathematica ...
Ben S.'s user avatar
  • 111

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