Questions tagged [summation]
Questions using the Sum command, especially for series and other algebraic objects, and related functions such as SumConvergence
931
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Check the convergence of double sum
I have the following double summations:
Sum 1 : $\sum _{p=0}^{k-1} \left(\frac{\sqrt{\frac{(p+1) \Gamma \left(p+\frac{11}{4}\right)}{\Gamma (p+2)}}}{(p+2) \sqrt{\Gamma \left(\frac{11}{4}\right)}}-\sum ...
- 185
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1
answer
61
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How to check two summands give same summation value without evaluating the sum?
It is easier for me to explain the question with the following toy example.
Suppose I have two summands,
Summand1 = n1 + 2 n2;
Summand2 = 2 n1 + n2;
Now, it is ...
- 1,092
3
votes
2
answers
316
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Double Summation over Lattice
I have a double lattice sum and I was wondering how I could calculate this with Mathematica. In particular, I have a function $F:\mathbb{R}^2 \times \mathbb{R}^2 \to \mathbb{R}$ which takes as ...
- 323
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0
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64
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How to calculate generalized discrete convolution without using DiscreteConvolve
I want to find the discrete convolution of two functions which potentially do not share a common domain. For example I have
...
- 2,425
0
votes
2
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79
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Kernel dies when trying to compute coefficients in a linear sum involving expressions like b[1,2][3,4]
The following happens on 11.0.1.0:
Have
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- 1,724
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1
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31
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How to resolve problem during summation of functions?
I am trying to find out the output of this basic problem but getting an error. If anyone can resolve this will be helpful.
...
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1
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1
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62
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How to symbolically manipulate the closed form series output from the easyFourier package?
EasyFourier by @xzczd is a nice package to obtain a Fourier series in closed form, e.g.
f = x^2
easyFourierTrigSeries[f, {x, -\[Pi], \[Pi]}, \[Infinity]]
However, ...
- 371
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0
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56
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How To Define Indexed Vectors
I have to define two 2-D vectors to be multiplied by a matrix and multiplied by several Clebsch-Gordan coefficients. Below are my definitions and my attempt at computing the sum.
...
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0
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0
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46
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Weird (erroneous) behavior in evaluating particular infinite sum
What is the cause of this behavior? Notice that in the result there is n which is the index of summation, so n should never ...
- 5,935
-1
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1
answer
96
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Summing functions in a Do loop [closed]
I can print these functions like this:
...
2
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3
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367
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How to ask Mathematica to subtract each adjacent pair in a list, and then, sum them?
If I have a list of numbers as (the number of elements in this list is even)
list={1,23,32,54,65,76,87,98,109,110,...}
How can I ask Mathematica to subtract each ...
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214
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0
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0
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133
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How to calculate this summation numerically?
I want to calculate this summation numerically:
$\sum_{n=1}^{10^{10}}\frac{1}{n^3\sin(n)^2}$
First I try
NSum[1/(n^3 Sin[n]^2), {n, 1, 10^10}]
however it gives a ...
- 503
2
votes
0
answers
75
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NSum complaining of being non-numerical
I am trying to evaluate the sum $\sum_{k,l=1}^{30}\frac{1}{(k^2+l^2+1)^{5/4}}$ so I write
NSum[1/(1 + k^2 + l^2)^(5/4), {k, 1, 30}, {l, 1, 30}]
but I get a message ...
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64
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Write code that finds the ripple of a function (existing code finds the wrong answer)
I have the following code:
...
- 1,941
0
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1
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62
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Determining the voltage ripple when the transient is over (mistake in result)
Well, I have the following code:
...
- 1,941
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1
answer
101
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Automatic summing of dummy indices [closed]
I have:
$$test1=t_{1,2} \delta _{1,a} x_{2,b} \left(-\frac{\partial L}{\partial x_{a,b}}\right)-t_{1,2} x_{1,a} \delta _{2,b} \frac{\partial L}{\partial x_{a,b}}$$
$$test2=t_{1,2} x_{2,a} \delta _{1,b}...
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2
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2
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265
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Sum over a list of indices
Suppose I have a sum like
$$ \sum_{i_1,i_2,\dots,i_n\geq 0} f(i_1,\dots,i_n)$$
How can I write this with Mathematica? In other words, is there a way of generalizing something like the following to $n$ ...
- 123
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0
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54
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Total of only positive (or negative) values in TimeSeries
I've a TimeSeries like the following one:
...
- 930
3
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1
answer
589
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0
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0
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54
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Issues in expanding expressions with formal sums
I have a very long expression involving formal sums to infinity, unfixed functions and several variables.
In this very long expression, I need a typical term, like
$\frac{6 A \sigma \sum _{n=0}^{\...
- 1
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4
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240
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Accurately computing $\sum_{j=2}^\infty \frac{(-x)^j}{j!} \zeta(j)$
I'm doing a sanity check of the following equation:
$$\sum_{j=2}^\infty \frac{(-x)^j}{j!}\zeta(j) \approx x(\log x + 2 \gamma -1)$$
Naive comparison of the two shows a bad match but I suspect one of ...
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10
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1
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225
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Hessian matrix with D and Sum Method->"Procedural"
Bug introduced sometime between 10.0.2 and 11.2 and persisting through 13.2.0 or later
Having just discovered Sum's ...
- 19.1k
1
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2
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171
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Mathematica's evaluation of nested summations
As suggested there, here is a copy of the question I've posted on Math.Stackexchange.
Suppose we want to count the number of instructions executed by the following Python code:
...
- 113
2
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2
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142
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Using `FindRoot` to solve over positive integers?
I need to solve for the smallest positive integer $s$ such that the following is satisfied for $p>1, n\approx \infty, \epsilon>0$
$$\frac{\sum_{i=1}^n \left(1-i^{-p}\right)^si^{-p}}{\sum_{i=1}^n ...
- 7,484
0
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0
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152
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How can I speed up this pdf path integration calculation with a slow recursive function with 40^4 summed terms in each iteration?
I am writing a path integration code for a numerical approximation to a probability density function.
I essentially take some initial continuous probability density function p0 and then perform a ...
- 21
2
votes
1
answer
137
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Slow Sum with Subscripts
Edit: My original question implicated D in the problem, but it seems unrelated, so I've removed that part of the question.
I am writing a function that uses ...
- 19.1k
0
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1
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87
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Why does summation over list elements are very slow compared to direct numbers?
Here I will provide a simple example of what I mean. Using ParallelSum with direct numbers is very fast as here
...
- 4,067
2
votes
3
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166
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Limit of empty sum
Why MMA delivers this result and how to interpret or reformulate it?
Limit[k Sum[1/i, {i, 1, k - 1}], k -> 0]
I would expect 0 as it is an empty sum.
MMA 12.1
...
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0
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1
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149
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Symbolic partial differentiation of a Lagrangian function including a summation
I'm using Mathematica to double-check that I correctly derived first order conditions for the models I'm researching. Before I get started, I wanted to actually teach myself how to use Mathematica, ...
4
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2
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110
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RSolve solves only one of two equivalent recurrences
I am having an issue with the RSolveValue/RSolve function. Specifically, Mathematica is able to correctly evaluate ...
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1
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88
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How to evaluate Sum with Singularities?
I derived equation of sum from the following problem,
$\int_{a}^{b}\sum_{n=0}^{\infty} cos^n(x)dx$.
Using the following definitions,
$cos(x)=\frac{e^{ix}+e^{-ix}}{2}$ and $(a+b)^n=\sum_{m=0}^{n}\binom ...
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3
votes
1
answer
135
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Quickly compute inverse summation
I'd like to look at behavior of $f(n)$ for the following $f$
$$\begin{array}{lll}
g(s,n)&=&\frac{1}{n}\sum_i^n \left(1-\frac{1}{i}\right)^s\\
f(n)&=&\text{smallest } s \text{ such that ...
- 7,484
2
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0
answers
84
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How to intelligently use FullSimplify and FunctionExpand to simplify complex sums
I am trying to find a compact form of some sums which is related with some Bayesian probability factor (not so relevant, if required further explanation please ask). The point is that I know that the ...
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3
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2
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207
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How to FInd the sum of odd divisor of a number in Mathematica?
So I want to find the sum of odd divisors of a number raised to some power.
$i.e.$ I want to find $\sum_{n=1}^\infty\sigma'_{-2k-1}(n)$ where $\sigma'_{-2k-1}(n) = \sum_{d|n, \text{d odd}} d^{-2k-1}$.
...
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1
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214
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Symbolic Mean and Variance Calculations
I need a tutorial that gets me started on basic symbolic calculations with random variables. My naive attempts did not get me far.
...
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0
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1
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49
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Simple expression involing Sum[] Mathematica fails to simplify [duplicate]
I have been trying to coax Mathematica to solve some equations involving expressions like Sum[A[t],t], with mixed success. One thing that really surprised me though ...
- 103
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1
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140
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Plot3d plots an empty graph [closed]
So I'm trying to graph a wave-type function using the following code:
...
3
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1
answer
79
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Summing list elements for given index tuple
Is there a more compact way of summing certain elements of lists together when given a tuple of which elements to sum. For example if I am given the list of size 8:
...
- 295
1
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1
answer
106
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Summation without writing term by term
https://mathematica.stackexchange.com/a/222410/73364
I have obtained the following code from the above link
...
- 1,225
1
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3
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70
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How to ask Mathematica to do the given operation for a set of parameters?
I have a set of numbers like this
s = {a, b, c, d, e, f, ..., g, h}
and I would like to ask Mathematica to do the following operation (to sum the subtractions of ...
user67849
0
votes
1
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441
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How to get Sum of array of integers?
This question seems easy but I am struggling with it now, I tried a few ways and check this solution as well but couldn't help me, please check and help if you are able:
So I need to save the sum of ...
- 499
1
vote
3
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126
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Infinite double sum with exclusion
I would like to evaluate the following sum (numerically will suffice):
$$
\sum_{m,n=-\infty,(m,n)\neq(0,0)}^{\infty}\frac{1}{m^{4}+n^{4}}
$$
I first tried to do
$$
\sum_{m,n=1}^{\infty}\frac{1}{m^{4}+...
- 973
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votes
0
answers
135
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Summation variables aren't recognised as dummy variables
I'm trying to write this expression
in Mathematica, and calculate the following quantity
However, when I tried the following
...
- 229
1
vote
0
answers
50
views
Large and infinite sums evaluated numerically
I am interested to learn when and how Mathematica is able to evaluate large/infinite sums numerically in reasonable time. I have found that it can evaluate
$$
\sum_{l=1}^{\infty}e^{il/2}H_{0}^{(1)}(l)
...
- 973
0
votes
0
answers
32
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Inequality programming involving sum compositions
$n=3$,
$m=3$,
$B$ - identity matrix $3 \times 3$
Trying to implement it in Mathematica, but can't figure out how to program the second term. The result is an error.
...
- 2,344
0
votes
1
answer
158
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How to plot a Sum function with Bessel function of the first kind [closed]
I have looked around for a code that can help to plot the magnitude and phase of the following sum
Sum[(BesselJ[n, r] e^(I n ϕ))/I^n, {n, -N, N}]
But I am not able ...
- 19
0
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0
answers
154
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Invalid integration variable/Raw object ... cannot be used as an iterator
I have a short code:
...
1
vote
1
answer
60
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ParallelSum issue inside package
I have the following very simple package with only one external function SumSeries[]:
...
- 1,092
1
vote
3
answers
209
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How to approximate the harmonic sum $\sum_{n=1}^\infty\frac{{4n\choose 2n}\overline{H}_{2n}}{n 2^{4n}} ?$
How to approximate $$\sum_{n=1}^\infty\frac{{4n\choose 2n}\overline{H}_{2n}}{n 2^{4n}} ?$$
Where $\overline{H}_n=\sum_{k=1}^n \frac{(-1)^{k-1}}{k}$ is the skew harmonic number.
The mathematica ...
- 445