# Tagged Questions

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### Einstein Summation - does the following equality hold: $a_{ij} x_i y_j = a_{ij} y_i x_j$

Does equality hold when $x_i = y_i$ and $x_j=y_j,$ and $i, j = 1, ..., n$.
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### Einstein Summation: How do I show $a_{ij} (x_i + y_j) \not= a_{ij}x_i + a_{ij}y_j$?

Einstein Summation: How do I show $a_{ij} (x_i + y_j) \not= a_{ij}x_i + a_{ij}y_j$?
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### Notation: need help to understand the notation in the following formula

E is just a function such that E1=1, E2=2 and so on. But my question is the part of on "arg" and "min". 1) so "arg" stands for the angle of complex number? this doesn't make any sense. 2）If I ...
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### Trouble understanding $\sum$ notation

Question: What does $$\left(\sum_{a, b, c}a\right)^2$$ mean ? The answer given is $(a+b+c)^2$. However, I am having trouble understanding this. I have seen this, this and this. But none helped. ...
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### Precise notation of a sum of a sequence

I need help in rewriting the support of a function $f$ in a more compact or precise way given its upper bound $b$ and lower bound $a$ as \begin{eqnarray} b&=&\max\left( \sum_{n}\alpha_n ...
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### Is there a way to denote the calculation $1+2+3+\dots+n$? [duplicate]

Since $n!$ represents $$1\cdot2\cdot3\cdots n,$$ I am wondering if there is a way to represent $$1+2+3+\dots+n?$$ What are some usual notations for the computation of some common sequences? Any other ...
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### Difference between $\lim_{n\rightarrow\infty}\sum_{k=1}^{n}a_k$ and $\sum_{k=1}^{\infty}a_k$

Is there any difference between $\lim_{n\rightarrow\infty}\sum_{k=1}^{n}a_k$ and $\sum_{k=1}^{\infty}a_k$? My example and thought: Let $a_n=n$ where $n\in\mathbb{P}$. $\mathbb{P}$ is the set of all ...
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### Doing an operation to every number in a subscript

I'm not good with words, and neither with math, but I'll do my best. (If someone has a better title for this then...). I've been learning about subscripts recently, and things like $\sum$ and $\prod$. ...
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### Multiplying subscripts

I'm not too good with math, but once in a while I like to fiddle around with it. But one question has been bugging me lately. Let's say I have $x_{1} = 1$, $x_{2} = 2$, etc, $x_{352} = 352$. Is there ...
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### A question regarding notation of equation

I'm reading a research paper, and, have come across this summation equation $$S_{2} = \sum_{N -1}^{j = 0}w_{j}^{2}\cdot$$ My question is: if j = 0..... N-1 do I ...
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### Notation for summing all elements under the diagonal of a square matrix

I have a simple question: What is the notation for summing all elements under the diagonal of a square matrix? I appreciate your help.
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### Summation of elements of a Set [Notation]

Is there any compact Notation to express the summation of all the elements of a set?
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### Does this summation index make any sense?

From my textbook, I have this summation: $$y_f(k) = \sum_{\tau = k_0}^{k-1}a^{k-1-\tau}g(\tau)$$ So far so good. But then there is a "change of variable" $\tau = \theta - m$ and the summation ...
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### How to find a summation of a sequence?

I am working in analyzing an algorithm in recurrence, but I end up in the following sequence: $$\frac5{2^6}n^2+\frac5{2^4}n^2+\frac5{2^2}n^2+n^2$$ I tried to make an equivalent summation but I ...
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### What does this notation (unmatched right parenthesis after a summation) mean?

My textbook contains this notation: $$\sum_{n=0}^{\infty} r^{2n}\cos n\theta \bigg) ^2 + \quad \sum_{n=0}^{\infty} r^{2n} \sin n\theta \bigg) ^2$$ What does this notation mean? Square the result of ...
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### When using sigma notation, why is “1” put as value?

First of all, I never really learned exactly what Sigma notation is, and although I understand the basics, there are some things that are confusing me. I'm trying to convert the following algorithm to ...
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### Sigma with Or Underneath

This is the notation found in Spivak's Calculus: Chapter 23: Infinite Series Theorem 9 What does $\displaystyle \sum_{i \text{ or }j > L} |a_i||b_j|$ mean?
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### Why is the upper bound of this statement always incremented by 1?

Why is "for j = 1 to n" translate to this? Why is the upper bound always incremented by 1? $$\sum_{j=1}^{n+1}1$$ Why isn't it $$\sum_{j=1}^n1$$ "for j = 1 to n" is written in pseudo code btw ...
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### 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 ...
I am trying to find the Fourier series of a 3D function, $e^{-\alpha(x^2 + y^2 + z^2)}$ with bounds $-\ell_1 < x < \ell_1$, $-\ell_2 < y < \ell_2$, $-\ell_3 < z < \ell_3$. I have ...
$\sum_{i=0}^{5}{i^2} = 0^2+1^2+2^2+3^2+4^2+5^2 = 55$ How to write this Sigma notation only for odd numbers: $1^2+3^2+5^2 = 35$ ?