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Questions tagged [summation]

Questions using the Sum command, especially for series and other algebraic objects, and related functions such as SumConvergence

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Matheamtica Junior on HPC

I am learning Matheamtica on HPC and have never used a linux system before. I have turned the style "input" into "code" and save the file as m format. However, the HPC does not work. The code is ...
3
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1answer
65 views

Multiply a Sum by a factor

A very simple question: How can I tell to Mathematica that: $\begin{equation} x*\sum_{k=0}^{\infty}\,b_kx^k=\sum_{k=0}^{\infty}\,b_kx^{k+1}\end{equation} $ I tried to multiply but Mathematica gives ...
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1answer
57 views

How does one use NSum within NIntegrate properly?

If I use symbolic integration for the following: Sum[Integrate[i + x, {x, 1, 7}], {i, 1, 7}] 336 as one can see it gives the answer as it seems to '...
2
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1answer
50 views

Error with NSum : it returns NSum::nsnum: Summand (or its derivative) f[n] is not numerical at point n=17

Consider the following example (I had a lot of trouble to find a minimal working example, I think it is compactified enough now). ...
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2answers
44 views

Sum up different arrays into a new array

I have a question regarding sums in arrays. So I have the following array: ...
2
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1answer
95 views

Calculation of sum $\begin{aligned}\sum_{k = 1}^{n - 1}\end{aligned}\left(1+\cos\left(\frac{k\,\pi}{n}\right)\right)^n$

Having established that Mathematica cannot calculate the following summation: sum = Sum[(1 + Cos[k Pi/n])^n, {k, 1, n - 1}] I implemented the classic "plan B", ...
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1answer
41 views

Modifying/optimizing a double sum with an If condition

I would like to better understand double summations where one of the sums depends on the upper limit of the previous sum. This appears frequently in representation theory (to the extent of my ...
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2answers
66 views

Apparent contradiction in double summation

I have two expressions which, if my maths is correct, should both be true. But Mathematica doesn't agree. I can take the expression E^(-n^3) out of the single ...
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1answer
59 views

Sum of powers of zero [duplicate]

I would like to calculate the following sum Sum[0^(k-a), {k, 0, Nin}] for a positive integer $a$. With considering $0^0=1$, my expected answer of the sum is $1$, ...
2
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3answers
114 views

Sum with variable terms to sum over

Suppose I have a polynomial like this: $$a=x_{j_1} + x_{j_1}x_{j_2} + x_{j_1}x_{j_2}x_{j_3} + ...+x_{j_1}x_{j_2}x_{j_3}...x_{j_n}$$ I want to create a function that takes this polynomial and does the ...
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1answer
267 views

Einstein summation convention for symbolic vector calculus

I am trying to do some vector calculus in Mathematica in index notation form because it gives a clear result that can be compared to pen and paper calculations. Since there is no built in Einstein ...
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1answer
60 views

Simplify multiple summations involving Kronecker deltas

Sorry if this has been asked before, but I couldn't find a specific answer to it. These work, i.e. they simplify: ...
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2answers
72 views

Collecting terms from expression with indexed functions

Say I have an expansion of terms containing functions y[j,t] and its derivatives, indexed by j with the index beginning at 0 ...
3
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2answers
154 views

Problem with extracting a constant multiplier out of sum

For a generic symbol A[i] 2 Sum[A[i], {i, 1, n}] == Sum[2 A[i], {i, 1, n}] does not return ...
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1answer
104 views

Checking an interesting result for a sum

If someone is curious I have solved it here: https://math.stackexchange.com/a/3242204/647013 This question is related to this post https://math.stackexchange.com/q/3241994/647013, but I am fairly ...
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25 views

What is the principal difference betwen two results of a seemingly similar sums?

Summing Sum[(a^2 + (b + n)^2)^(-1), {n, -Infinity, Infinity}] gives $$\frac{\pi \sinh (2 \pi a)}{a (\cosh (2 \pi a)-\cos (2 \pi b))}$$ whereas summing <...
3
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1answer
64 views

What is the meaning of True in my result? [closed]

When I do the sum Sum[(a + (b + π n)^2)^(-1), {n, -∞, ∞}] the result reads $$\begin{array}{cc} \{ & \begin{array}{cc} \frac{\coth \left(\sqrt{a}+i b\...
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0answers
19 views

Incorrect result with very simple in(de)finite sum of conditionals [duplicate]

The results of both Sum[If[OddQ[2 m - 1], 1, 0] q^m, {m, n}] and Sum[If[OddQ[2m-1],1,0]q^m,{m,\[Infinity]}] are 0 (in ...
4
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1answer
202 views

How to approximate the partial sum formula of a summation to all real numbers using Mathematica?

I am sure one has to use indefinite sums and the Euler-Maclaurin formula. $$\sum_{x=0}^{n} f(x)=\sum_{x}f(n+1)-\sum_{x}f(0)=\int_{0}^{n+1}f(t) \ dt -\frac{1}{2}f(n+1)+\left(\sum_{k=1}^{\infty}\frac{...
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1answer
230 views

Why is the result of a Cesaro regularized sum dependant on a mathematically redundant parameter?

I am trying to determine the series $\qquad \sum_{k=0}^\infty {\rm myCsc}(x,\,\epsilon)\,{\sin(k\,m_C + a_C+\frac\pi 4)}$ where $\qquad myCsc(x,\epsilon))= \begin{cases}i\,\epsilon & 0 \...
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2answers
89 views

Sum not recognized as a linear operator by Solve

When I try to solve an equation with a constant under the summation sign, Mathematica does not factor the constant out of the summation and fails to solve a simple equation. How do I make ...
3
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1answer
192 views

How to evaluate sum with one million summands?

For a research project I am working on currently, I need to do a very simple and straightforward calculation. Unfortunately, I do not know how to include Mathematica code here, but it is very short ...
4
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3answers
825 views

How to speed up large double sums in a table?

I am calculating a 3-by-3 matrix whose elements are given as follows: $$ M_{mn} = \frac{1}{N}\sum_{i=1}^N \sum_{j=1}^N (r^i_m - r^j_m)(r^i_n - r^j_n) \tag{1} $$ where $N$ is the total number of ...
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2answers
424 views

How to sum elements of a list of lists?

I know, the title may seem complicated. I have this list: myList = { {1, 0},{2, 3},{4, 1} } I want to sum all the sublists (element by element) to obtain this ...
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1answer
92 views

Efficiently define a function as the numerical result of infinite sums

I want to approximate the solution to the following sum, in such a way that I can plot the function for the variable $\phi$, for a fixed value of $\mu$. \begin{equation} f(r(\phi), \mu)=4 e^{-\mu ...
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1answer
81 views

Using the Sum function square the sums of numbers

How do I use the Sum function for adding and squaring consecutive terms? It's an exercise from Wolfram Challenges. I want to write my own function that uses the Sum function to get the sum of (1+2)^2 ...
2
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0answers
63 views

Flaky pattern-matching for Mittag-Leffler sums?

This sum correctly gives the Mittag-Leffler function: Sum[z^k/Gamma[α*k + α], {k, 0, ∞}] MittagLefflerE[α, α, z] Simply factoring the argument of ...
2
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2answers
131 views

FullSimplify a trigonometric expression doesn't work as expected

I know this kind of question is frequent asked, yet each case has its own particularities. I will show my problem. I define the following: ...
2
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1answer
40 views

Clarification on how Total[] can be used on multi-dimensional array

I have a rank 5 tensor that ultimately I want to modify so that for the first 3 dimensions, each element is summed together. The result will be a rank 2 tensor whose elements are the summed totals ...
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0answers
98 views

Clebsch Gordan coefficients

I'm trying to compute various sums which contain some CG coefficients, where the sum runs over the indexes m1,m2,m corresponding to each of the three angular momenta j1,j2,j. The thing is that when I ...
2
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1answer
73 views

How to speed up summations with many list callings?

I am trying something similar to the following code with NN as large as a few hundred (at least 100). Now it's very slow and most time is spent on calculating the ...
2
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1answer
248 views

The sum of digits of Mersenne primes

I have problem to calculate the sum of digits of the mersenne primes $M_{57885161}$ , $M_{74207281}$ , and $M_{77232917}$. I'm not a 'computer guy', but I know that the sum of digits of $M_{82589933}$ ...
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1answer
40 views

Handling Errors in Slowly Converging Dirichlet Beta Infinite Sum

I have tried to calculate the following slowly converging double sum in Mathematica 11.3 $$\sum _{k=1}^{\infty } \left(\frac{ 1}{(2 k-1) (2 k+1)} \left(\sum _{n=1}^{\infty } \frac{(-1)^{n-1}}{(2 n-1)...
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1answer
66 views

Plotting a series

I'm trying to find a way to plot the sum of a series from n to nmax. Here is the code for the series: ...
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2answers
110 views

Summation over an index and a set

I have an index CC and a set of values CM, and c is an element of CM and ...
2
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0answers
408 views

Faster ways to compute recursive summation [on hold]

It takes a long time to compute the summation below, and I'd like to know if there are some better ways to compute things faster. I have used $3$ ways to calculate, but they are very unsatisfactory. I ...
3
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5answers
211 views

Calculating the Dottie number using an infinite series

The Dottie number is the solution to the equation $\cos(x) = x$ It is approximately equal to $0.739085133215160641655312.$ This number can be expressed analytically in the following form (see this ...
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0answers
72 views

Infinite sum with recursive coefficients

Mathematica can handle infinite sums like Sum[ x^k/k!, {k, 0, Infinity}] (* Exp[x] *) Suppose I only know a recursive definition of the coefficients ...
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0answers
74 views

Sum over cyclic permutation of indices

To define the Schouten bracket I need to be able to sum over a cyclic permutation of the indices: $$ [\Phi,\Xi]_S=\mathfrak S_{i,j,k} \left(\Phi^{is}\partial_s\Xi^{jk}+ \Xi^{is}\partial_s\Phi^{jk}\...
1
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1answer
82 views

Plotting double series

I am new and hoping a warm welcome from this platform. I am trying to plot the graph of double series in one variable $$ \sum_{k=0}^{\infty} \sum_{j=0}^{\infty} C_{k,j} \exp(- 3^k 1.5^{j} x)$$ ...
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1answer
56 views

Replace constant in summation function using replace or If or /

Hi i how do i replace constant for k in this summation. For following: Even 2*n Even replace k by a Even 2*n+1 Odd replace k by b Here is the code ...
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0answers
94 views

Finding general forms of sums in Mathematica

A general form can be obtained for some sums with binomial coefficients. Mathematica is able to find these general forms for some of the simplest sums. For others the output contains for instance ...
2
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2answers
50 views

Is it possible to make a series read a separately defined set of values?

I would like to plot a function with a sum in it. Here is the function: $$v(k) = \sum_{j=1}^k \frac{v_E \cdot m_j \cdot c}{m_j(1-c)+\sum_{i=j+1}^n m_i} $$ As you can see, the problem is that I have ...
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2answers
303 views

Sum a certain hypergeometric-function-based expression pertaining to an integration problem

I would like to sum over the index $h$ from 3 to $\infty$, the expression ...
1
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3answers
278 views

Simplify Kronecker Delta expression

How to obtain Kronecker delta summation rule using Wolfram Mathematica: $$ \delta_{ij}\delta_{jk}=\delta_{ik} $$ The following code does not produce the result. ...
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3answers
305 views

Subscripted variables with changing subscript

When I want to sum over indexed variables, indices being subscripts, the result works as expected, however, upon loading the Notation package, it doesn't. See below As one might have expected from ...
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0answers
94 views

Summation involving 2F2 hypergeometric function

Trying to simplify the following sum: $$ \sum_{i=0}^n\frac{z^i}{(n-i)!}\,\frac{1}{(1+a)_i\,(1-a)_i}\sum_{j=0}^i(-1+a)_j\,(-1-a)_j\frac{(-z)^j}{j!}, $$ where $n=1,2,\ldots$, $z>0$, $0<a<1$, ...
2
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3answers
160 views

Force a sum to be simplified

I want to force this sum to be simplified to 1 Sum[Cos[(Pi*l*(2*m + 1))/(n + 1)], {l, 0, n}] Only DiscretePlot3D gives the correct result showing all point to 1
-4
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2answers
91 views

Wolfram|Alpha not able to graph sum_(n=0)^∞ (-(ExpIntegralE[-n, (-1 + n) Log[x]] Log[x]^(1 + n))"? [closed]

I know for a fact that nothing in my expression is wrong, then why cant Wolfram|Alph graph: sum_(n=0)^∞ (-(ExpIntegralE[-n, (-1 + n) Log[x]] Log[x]^(1 + n))) ? ...
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3answers
126 views

Handling cases of cross terms for multi-sums

I have expressions consisting of many multi-sums and I would like to extract cross terms out of them. Consider a simple example: $$ \sum_{m_1=1}^M \sum_{m_2=1}^M \sum_{m_3=1}^M \sum_{m_4=1}^M (x_{m_1}...