# Questions tagged [products]

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

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### Product[(n - 1)/n, {n, 1, 1 k}] [closed]

Could someone explain why Product[(n - 1)/n, {n, 1, 1 k}] always returns zero? I tried using different equations and it worded fin but when I use $\frac{n-1}{n}$ it won't work.
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### Smoother ways for setting up a Product function with j=0 and j != i

I want to implement a Product function, particularly the Lagrange polynomial $\ell_{i}(x)=\prod_{j=0 \atop j \neq i}^{n} \frac{x-x_{j}}{x_{i}-x_{j}}$ Are there ways to implement the "not equal" ...
144 views

### Closed form of product of Gamma function

Mathematica recognizes this closed form \begin{align} \prod_{k=1}^{n-1}\sin(\pi k/n) &= 2^{1-n}\,n \end{align} just fine: but fails on this one despite that this expression also has a known ...
37 views

### Simplifying the dot product [closed]

Why does the code D[x.x, x] /. {1. x -> x, x .1 -> x} gives 1.x+x.1, while ...
44 views

### How to evaluate an expression [closed]

I have a 3-dimensional array of numbers say A. I want to evaluate the following expression. $\displaystyle\sum_{\sigma,\tau \in S_6}(\Pi_{i=1}^6A(i,\sigma(i),\tau(i)))$. $S_6$ is the symmetric group ...
149 views

### Why is this product equal to zero, when the correct result is 2+GoldenRatio?

Consider the following product $$\prod _{k=2}^{\infty } \frac{1}{1-\frac{\left(\frac{1}{2} \left(\sqrt{5}-1\right)\right)^k}{1-\left(\frac{1}{2} \left(\sqrt{5}-1\right)\right)^{2 k}}}$$ Mathematica ...
52 views

### How to multiply the elements of each site of tensor products to each other while using symbolic representation?

If I have, say three sites in a symbolic operator which is of the form A = a⊗1⊗c and I want it to act on another operator B = a1⊗b⊗1 in order to find the commutator A.B - B....
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### Product from max to min [closed]

Product[f[i], {i, 1, 4}] gives us f f f f Is there any way I can take the product it will give something ...
78 views

### Series of a product of series

I am writing a code where I have to multiply large series truncated at some order, say 100. As a result I want again a series up to order 100, and I want to get it in the fastest way. I have tried a ...
214 views

### How to calculate $\displaystyle \prod_{p}\frac{p^2+1}{p^2-1}$?

When I input $$\prod _{p=2}^{\infty } \text{If}\left[\text{PrimeQ}[p],\frac{p^2+1}{p^2-1},1\right]$$ in Mathematica 12.0, it gives out the value $1$. The result is ridiculous, for that according to ...
52 views

### Return last value of While function

I want to make a function that performs a multiplication with Inner i number of times using a ...
42 views

### Set default product

I want to set a default product in Mathematica in place of the standard product. Specifically, I want to change the standard product for CenterDot so that when I ...
80 views

### Summation and product term expressed in Mathematica [duplicate]

I have the following term which I would like to express correctly in Mathematica: $$\sum_{i=1}^{m}\frac{1}{\prod_{j=1,j\neq i}^m(\rho_i-\rho_j)}$$ This means that for $m=3$ for example you should ...
135 views

### How to write down a product with omitted terms?

I have the following term which I would like to express correctly in Mathematica: $$\prod_{j=1,j\neq i}^m(\rho_i-\rho_j)$$ Can you please help?
119 views

### Outer (dyadic) product between vectors of the same index in two lists

I have two lists of vectors and I want to take the outer product between elements in the lists of the same index. Using either Outer or TensorProduct works for e.g. the first two indices: ...
86 views

### Where is the “mistake in the recursion” while there is no recursion? [closed]

So my code is as follows xi = Exp[2*Pi I/13] tauA = xi + xi^(-1) sigma[tau_, n_] := tau^n Product[(x - sigma[tauA, i]), {i, 3, 8}] // FullSimplify This should ...
83 views

### How to create a dot product version of the product function

I would like to create a function to matrix multiply (dot product) n matrices together, where n is large, for example M1*M2*M3*M4*M5*...*Mn I know there is the 'product' function that can do this ...
38 views

### How to PowerExpand a generic Product?

I have: PowerExpand[Log[Product[f[i], {i, 1, n}]]] // InputForm (* Output: Log[Product[f[i], {i, 1, n}]] *) However, I would expect to get the following as the ...
223 views

### Dot product result has wrong dimension [closed]

I'm doing a small project and I've encountered a problem while using Mathematica. I should mention that I'm kinda new to this software, so maybe it's just something I haven't grasped yet. Anyway, I ...
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### How to put conditions on indices of product

I'm trying to solve for the Lagrangian form of the interpolation polynomial. Right now, I'm just trying to solve for the $l_i(x)$ values which are equal to \$l_i(x)=\prod_{j\neq i, j=1}^{n}{\frac{x-x_j}...