Questions tagged [summation]
Questions using the Sum command, especially for series and other algebraic objects, and related functions such as SumConvergence
927
questions
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I can't solve this problem [closed]
$$\sum_{k=1}^{\infty}\ln(\frac{(k + 1) (k + 3)}{(k + 2) ^ 2})$$
The answer is = ln(2/3)
Can you please help me?
- 9
0
votes
0
answers
30
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Calculating minimal unknown coefficients of a sum
I have a problem, where I have to find the minimum of a function with a sum in it (coefficients are unknown):
psi[x_] := 1 + a*x + b*x^2 + c*x^3 + d*x^4 + ...
...
0
votes
0
answers
40
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Hadamard’s Theorem from Gradshteyn and Ryzhik's handbook [migrated]
In the book http://fisica.ciens.ucv.ve/~svincenz/TISPISGIMR.pdf on page 1077 I found one interesting theorem:
I took an arbitrary matrix and tested this theorem. The result is the following:
...
- 2,304
1
vote
0
answers
31
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Simplifying symbolic sums using KroneckerDelta
I am trying to use Mathematica to simplify a symbolic expression of the following form
$$ S_i = \sum_{n_1 = 0}^\infty \sum_{n_2 = 0}^\infty \ldots \sum_{n_M=0}^\infty n_i \times \Big(
\sum_{j = 1}^...
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2
votes
3
answers
171
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Compile integer functions
I need to speed up a function that uses Binomial and QuotientRemainder. I used Compile, but ...
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3
votes
3
answers
104
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Summation over a restricted domain
i would like to sum n=0 to n=(some value) over all integers except those that are generated by some function with integer inputs and outputs, like f[n]=(n^2+3n)/2
so it would sum when n=0, n=1, skip n=...
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1
vote
1
answer
131
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Is there a builtin command or a workaround to generate a nested sum (of apropriate level) from an expanded expression?
I have the following output from some Mathematica manipulation of nested sums. Does Mathematica have a command or combination of commands that recovers nested sums from the expanded form?
$$\begin{...
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2
votes
1
answer
36
views
1
vote
2
answers
106
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How to have index of summation equal to all $n$-tuples $\left(b_i\right)_{i\le n}$ with $\sum ib_i = n$ and $b_j$ fixed?
Let $T_n$ denote the set of $n$-tuples $\left(b_1, \ldots, b_n \right)$ of non-negative integers such that $$\sum_{i=1}^{n}ib_i=n.$$ I am trying to simplify the sum (whose indicies depend solely on $n,...
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3
votes
6
answers
618
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How to ask Mathematica to compute the given sum of the differences of the numbers of the given two sets?
I have two sets of real numbers, say,
set1= {b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11}
...
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2
votes
1
answer
184
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Mathematica not able to output simple expressions for numerical sums
I am currently completing a project which involves various numerical sums, and I am trying to use Mathematica to evaluate them and obtain simple analytic results. For example, one such sum is
$$f_{(s,...
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0
votes
1
answer
66
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Finite result under "Integrate" while infinite under "NIntegrate" of a complicated integral with "NSum"
I have been trying to compute the following complicated integral along with summation, details codes/function of which is given below:
...
0
votes
0
answers
17
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Generating a 3 variables polynomial with constraints on 2
This post is a follow-up of Generating a 2 variables polynomial with constraints.
I would like to generate automatically a polynomial in three variables $(s,t,u)$ which is symmetric under the exchange ...
0
votes
1
answer
41
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Generating a 2 variables polynomial with constraints
I would like to generate automatically a polynomial in two variables $(s,t)$ which is symmetric under the exchange of those variables. There are three kinds of terms; at order $k$, we have
$$(s+t)^k, \...
0
votes
0
answers
32
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how to use DiscretePlot to graph multiple partial sum functions?
I am supposed to "Make a table that shows {k,s1[k],s2[k],s3[k],s4[k],s5[k]}, for k from 1 to 50, and display as a Grid." but I have literally no idea how to do this (I'm not good with ...
1
vote
0
answers
53
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Mathematica incorrectly claims an infinite sum doesn't converge
When I compare the output of the following commands I get contradictory results:
Sum[BesselJ[k, 1], {k, 0, Infinity}]
NSum[BesselJ[k, 1], {k, 0, Infinity}]
The ...
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votes
0
answers
93
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Recursive Sum not evaluating correctly
I'm trying to evaluate the following sums that nest into eachother:
$$
m_k=\frac{k}{k-1} \left(e^{\gamma}+ \sum_{i=1}^{k-2} {k-1\choose i} \frac{m_i}{i} \right)
\\
m_1=e^\gamma
$$
and
$$
\kappa_n = ...
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1
vote
0
answers
82
views
Internal variable in Sum inside a function [closed]
I am writing a simple function which performs a sum, but run into an unexpected answer.
...
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2
votes
1
answer
103
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Warning message when summing from a elements in a list
Why does adding two elements from a list as follows:
test = {1, 2};
NSum[test[[n]], {n, 1, 2}]
lead to the warning "The expression n cannot be used as a part ...
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6
votes
4
answers
340
views
Sum indexed over set
Say I have sets = {{a,b},{c,d},{e,f}} and I want to compute a sum like f[a,b] + f[c,d] + f[e,f]. One way to do this is to do
<...
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2
votes
0
answers
31
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Can we approximate a matrix power series like NSum does?
Essentially, the following does not work, and I'm wondering if it can be made to:
NSum[ MatrixPower[B,n], {n,0,∞}]
(Here B is a ...
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0
votes
1
answer
48
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Couldn't compute the coefficients of this series
Mathematica doesn't expand the series of this function (I'm using Wolfram Cloud version)
...
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2
votes
2
answers
85
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Pattern or ForAll statment in Assumptions
I would like to simplify an expression like
$\sum _{i=1}^k \sqrt{a_i^2}$, with the condition $\forall _{i\in \mathbb{Z}_{>\, 0}}a_i\in \mathbb{R}_{>\, 0}$ and with $k$ being undefined, which ...
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11
votes
1
answer
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2016 Putnam B6 difficult summation problem
Problem B6 on the 2016 Putnam exam is to calculate:
$$\sum\limits_{k=1}^\infty \left( \frac{(-1)^{k-1}}{k} \sum\limits_{n=0}^\infty \frac{1}{k 2^n + 1} \right)$$
The direct approach
...
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1
vote
2
answers
92
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Recursion with Sum
Using RSolve I tried without success to convert the recursive relation to a non-recursive function. How can I do this?
...
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3
votes
2
answers
201
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How can I get simplified answer for SUM?
I need to get the simplified answer after adding few SUM. In my code below, I know we have to define k ahead, so it will be unified and recognized for both, but I need it to be somehow symbolic, I ...
- 477
0
votes
1
answer
39
views
DiscretePlot of a function containing Nintegrate under Sum
I am trying to get DiscretePlot of the following integral containing laguerre polynomial, the Mathematica code of which is given below:
...
3
votes
1
answer
117
views
Apply condition to sum
I have this simple question, given the following sum: Sum[A[i][j][k],{j,0,10},{k,0,10},{i,0,5}]
I would like to apply the condition
$ A[i][j][k]=A[i][k][j] $
How ...
- 137
0
votes
0
answers
31
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"ListPlot" of some probability distribution of a function under "NSum"
Sir,
While trying to Listplot the Probability distribution of a function under command NSum, it shows some error messages and no plot is shown.
the details of the inputs written in mathematica along ...
3
votes
1
answer
72
views
Apply relationships to coefficients
I have the following sum:
s = Sum[Sum[Sum[Sum[A[i][j][k][l],{k,-10,10}],{j,-10,10}],{l,0,4}],{i,0,4}]
where the number of terms is where the number of terms is <...
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2
votes
1
answer
125
views
Calculation of average of sums is very slow
I have these functions
f[x_, n_] := 4/\[Pi] Sum[Sin[(2 k + 1) x]/(2 k + 1), {k, 0, n - 1}];
\[Sigma][x_, m_] := 1/m Sum[f[x, k], {k, 1, m}];
If I do:
...
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votes
1
answer
63
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How to write the code for polynomial $\sum^{\infty}_{j=0} \sum_{x_1+x_2+x_3=j}$ [closed]
Hellow, how to write the code of $\sum^{\infty}_{j=0} \sum_{x_1+x_2+x_3=j}$.
Here is the complete equation.
$$\sum^{\infty}_{j=0} \gamma^j \{ \sum_{x_1+x_2+x_3=j} \frac{(\frac{i}{2})^{x_2}(-\frac{3i}{...
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2
votes
1
answer
90
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Evaluate a double sum using Mathematica
I am evaluating using Mathematica, the double sum $\sum_{u=0}^\infty \lbrace \sum_{k= u+1}^{u+y}[\dfrac{(1-a)}{4} (3/4)^k + 3a[(\dfrac{1}{2})^{k-1} - (\dfrac{3}{4})^{k-1} ]\rbrace $, where $'a' $ is a ...
- 53
2
votes
3
answers
147
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Multiple Plots over non-consecutive integer parameter values
The following is a simple illustration of the difficulty I have encountered with multiple plots on the same diagram. The reason for trying to overcome (understand) the difficulty is more involved and ...
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2
votes
1
answer
107
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Accelerating sum over permutations of matrix elements
I am trying to short-cut the use of a CoefficientArrays call by manually calculating the resulting matrix of coefficients myself (this avoids using symbolic arrays ...
1
vote
1
answer
107
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NDSolve issue with summation
I have the following equation I am trying to plot,
$r''=f(r)+\sum_{n=1}^{\infty}a^n \frac{d^n}{dt^n}(f(r))$
and $r$ is a vector in $(x,y,z)$ that are time dependent. I wrote the code as follows,
...
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2
votes
0
answers
70
views
Why cant this sum expand to zero? [duplicate]
why cant this sum expand, and get the result zero? I want to prove something with symbolic equations in mathematica, but there seem to be not many tuturials about this area.
...
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2
votes
2
answers
494
views
How to code a sum in Mathematica and how to solve it?
I'm trying to find the coefficients of the Radau IIA Runge Kutta Implicit scheme.
Those Runge Kutta schemes have Butcher tableau consisting of Cs, As, and Bs.
article
I have already computed the Cs as ...
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3
votes
2
answers
173
views
Code for multiple sums
Please consider the following code. The definition of f depends on the code here and works correctly on its own. The trouble arises when calling F (which uses <...
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vote
1
answer
82
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Extracting powers of a sum
Given a sum in the form
Sum[n^k, {k, kl}]
for some natural n and natural list kl, is it ...
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0
votes
0
answers
69
views
Mathematica Can't Compute Sum?
I am trying to calculate a complicated Clebsch-Gordan sum in which appear also a dot product of vectors. However, when I run the code, Mathematica just won't compute anything, even if I let it run for ...
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2
votes
2
answers
154
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Evaluating sums with spherical Bessel functions
I'm running Mathematica 13.0, student edition, on Windows. In physics, the total scattering cross-section of plane waves off a hard sphere of radius $1$ is
$$\sigma(k) = \frac{4 \pi}{k^2} \sum_{l=0}^\...
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1
vote
0
answers
94
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Suggestions to simplify and perform the summation of a complicated expression
I have a very complicated expression involving Hermite polynomials of complex variables, exponential and hyperbolic functions. Since it is too long to be pasted here, you can find the expression here.
...
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1
answer
59
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How can one plot a sum in mathematica? [closed]
I would like to plot the following answer to the heat equation,
Sum[(((-1)^n - 1)/n^2) Cos[n x] Exp[-(n^2 t)], x]
But since it is a sum, it does not appear to work....
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1
vote
0
answers
55
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Do summation if factor does not depend on index
I have the following sums $$\sum _{j=0}^{n-1} \left(\sum _{c=1}^K \left(\sum _{b=1}^K m[b]^2\right)\right)$$ or $$\sum _{j=0}^{n-1} \left(\sum _{c=1}^K \text{$ n$}[c]\right)$$
where $m[b]$ and $n[c]$ ...
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4
votes
1
answer
188
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An unclear Mathematica result for Borel summation
Summation of divergent series
is applied in dynamical systems, q-difference equations, and mathematical physics nowadays
(for example, see that book for info),
this is not an old-fashioned topic.
...
- 21k
6
votes
1
answer
113
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User plug-in methods for SumConvergence
@Валерий Заподовников remarks:
BTW, it is also quite bad that Mathematica does not have Bertrand test.
Is there a way to extend the convergence tests in ...
- 226k
1
vote
0
answers
132
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What's the command for high approximation up to 50 digits?
I am trying to find the numerical value of $\displaystyle \sum_{n=1}^\infty \frac{e^{-n^2/\pi^2}}{n^2}$ up to 50 digits. I used
...
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5
votes
1
answer
420
views
Fast double sum involving Kronecker symbol
I have three lists
$$A=\{\alpha_1...\alpha_N\}$$
$$B=\{\beta_1...\beta_N\}$$
$$M=\{M_1....M_N\}$$
In practice $\alpha_i$ and $\beta_i$ are complex numbers with modulus smaller than 1. The $M_i$s are ...
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0
votes
1
answer
118
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Parallelize for loop in mathematica
I have the following code which essentially consists of a first for loop that iterates through a very large number of rows and a small for loop that iterates through a small number of columns. The ...
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