Questions tagged [products]
Questions about the use of `Product`, `NProduct`, and other types of multiplication, like `Dot`.
122 questions
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How do we find an asymptotic approximation of the function $\mathbf{P}(r)=\left(t_1+\prod\limits_{k=1}^{r}(t_2+k^{s})\right)^n$?
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 ...
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159
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How to syntax products and append each result to a table?
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 ...
6
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1
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463
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Kronecker product isn't behaving as I'm familiar with
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 <...
6
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3
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474
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Speeding up multiplication of matrix arrays by parallelization?
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 ...
1
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1
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141
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How can I write a single pattern for replacement for a nonlinear change of variables
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 ...
1
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1
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202
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Trouble in normalising two pairs of vectors
In the following code, I have two pairs of vector u0,u1 and v0,...
1
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143
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Are there built in vector cross product identities?
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 ...
2
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2
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114
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How to use these many conditions inside product?
I have tried all the way but I could not find a code for that line. It is consisting of three conditions.
2
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3
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177
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How to verify a FactorialPower identity?
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}] ...
6
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3
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511
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Why do I get different results for the products of two identical expressions?
I have two expressions with the Gamma function that are identical:
...
6
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2
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235
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Pattern recognition for products of variables
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}
...
2
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0
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85
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Expanding Pochammer symbols/Gamma function for simplifying expressions
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-...
2
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3
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437
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Simplifying products of DiracDelta
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
$$\delta(z-2)\delta(k-5)\delta(...
1
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0
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88
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Plot of some complicated functions containing special functions under both Sum and Product
I am trying to plot the $|f(\theta,\phi)|^2$, where the expression of $f(\theta,\phi)$ is as under:
$$ 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
\...
1
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164
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Taking the derivative of a product
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 ...