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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How to simplify a summation using mathematica

I have the following summation I would like to simplify: $f(y)=\frac{1}{\left(2^{N}-1-N\right) \sqrt{2 \pi}} \sum_{k=2}^{N} \frac{\left(\begin{array}{l} N \\ k \end{array}\right)}{\sqrt{k \sigma^{2}+1}...
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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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2answers
109 views

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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87 views

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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37 views

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 ...
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1answer
51 views

Plot3d plots an empty graph [closed]

So I'm trying to graph a wave-type function using the following code: ...
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1answer
42 views

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: ...
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1answer
92 views

Summation without writing term by term

https://mathematica.stackexchange.com/a/222410/73364 I have obtained the following code from the above link ...
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3answers
64 views

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 ...
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73 views

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 ...
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81 views

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}+...
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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 ...
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43 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) ...
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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. ...
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1answer
71 views

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 ...
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1answer
35 views

ParallelSum issue inside package

I have the following very simple package with only one external function SumSeries[]: ...
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3answers
134 views

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 ...
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Replacement of functions bound by sums and integrals in NCAlgebra

I want to use the NCAlgebra package to do some simplification on non commutative expressions involving integrals. For example, one such expression would be $$ I=\left(\int f(x)g(x) dx\right) * h $$ ...
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129 views

How to sum over $\mathbb{Z} \times \mathbb{Z} \setminus \{(0,0)\}$? [closed]

I want to sum over $\mathbb{Z} \times \mathbb{ Z} \setminus \{(0,0)\}$ . So, something like Sum[f[m,n],{m,-Infinity,Infinity},{n,-Infinity,Infinity}] but I want to ...
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1answer
40 views

Guess the next number formula [closed]

I have a sequence of numbers such as {1,2,4,8,16} The goal is to create a polynomial f(x) such that: f(0)=1, f(1)=2, f(2)=4, f(n)=nth item on the list I found this function which claims to do exactly ...
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1answer
51 views

Sum over multiple values falsely returning 'Indeterminate' [closed]

I have a conditional expression which depends on three variables, say x, y and z (all ...
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2answers
105 views

How to perform summation over specific columns of a table?

Consider the following table: ...
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1answer
39 views

Function as a sum over a list of functions

I would like to evaluate the following function q[beta_, gamma_] := Sum[R[[n, 3]]], {n, 3}]; q[Pi/3, Pi/4] Over the matrix ...
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59 views

Checking the formula of the square of a sum

The square of a sum reads $$\left(\sum_ia_i\right)^2=\sum_ia^2_i+2\sum_{i<j}a_ia_j$$. In Mathematica code for i=1 to 5 we get: ...
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80 views

Finding the exact symbolic formula for a function defined recursively

Let me introduce the problem. I have the following functions; The first one is defined recursively $h(i,j):=\frac{i-1}{j+1}h(i+2,j-2)$ and $h(i,0)=1$ where $i$ and $j$ are even integers, greater than $...
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Analytically express chi-square sum and solve

I have an expression: chisq[f_, x_, y_, e_, pars__] := Sum[((y[k] - f@@Join[{x[k]},pars])/e[k])^2, {k,1,n}] which should work for any function that has ...
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1answer
36 views

Determine the argument of the table such that two tables have the same value

Suppose i have A:=Plus @@ Table[2 (Pi/n) (i + 4), {i, 0, n/2, 1}] B:=Plus @@ Table[ x , {i, (Pi/n), (n/2 + 1) (Pi/n), (Pi/n)}] i need to determine the argument of ...
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How do you Sum with conditional iterators in WL?

Consider the following simple Sum: Sum[Binomial[n, n1], {n1, 0, n, 1}, Assumptions -> n ∈ PositiveIntegers] 2^n This of ...
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1answer
33 views

using a list of parameters in NSum [closed]

I am trying to make a function that uses NSum, that takes a list of parameters. But NSum doesn't appear to play nicely with lists. A minimum working example is: ...
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198 views

How to get the right approximation for a series involving the harmonic number?

The right numerical value of the closed form of $\sum_{n=1}^\infty\frac{4^n H_n^2}{{2n\choose n}n^2}$ is $40.66752074791188333...$. I tried to verify this result on Mathematica using the command: <...
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77 views

Computation of infinite series containing Zeta function

(this is my first question on this forum I'm totally inexperienced in mathematica) Consider the given alternating series: $$f(x) =\sum_{n=0}^\infty \frac{2a_n(x-1)^{2n+1}}{\zeta(-2n-1)}$$ Here, $a_n= (...
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67 views

How would I graph this function on Mathematica?

I could graph 1/n^2, but I don't understand how to graph the fractional part (x).
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84 views

Does Mathematica have a problem with sums involving Stirling numbers of the second kind?

In one of my calculations, I run the command: Sum[(StirlingS2[k - 1, 4] + StirlingS2[k, 4])/6^k, {k, Infinity}] Surprisingly, ...
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42 views

Evaluation of a double summation invovlving hypergeometric and exponential functions

I am trying to compute the following double summation over the indices, $m$ and $n$, which involves the hypergeometric function, ${}_2 F_1$, an exponential function and, factorials as a part of a ...
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1answer
134 views

How does Mathematica evaluate these sum and integral?

How does Mathematica internally evaluate the following (interrelated) sum and integral, and how does it do the subsequent simplification? (I mean, based on what mathematical facts?) ...
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28 views

How do I plot various values of the partial sums for a function with 2 variables?

This is what I have tried so far. I have a function defined as the below: ...
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23 views

Why summation of matrices in the MatrixForm gives wrong result? (an example is given) [duplicate]

I want to calculate the sum of two matrices, doing that in MatrixForm, I get which is wrong, but writing them as ...
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2answers
57 views

How to collect coefficients that has summation in ODE

I have the following equation, equation= x''[t]+a*x'[t]+b*x[t]+c*y[t]+d*u[t]+e*v[t]+Sum[f[i]*x[t]+g[i]*u[t]+h[i],{i,1,n}]+k When I collect the coefficient of each ...
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75 views

How to sum the KroneckerDelta[] in equation?

How to sum the KroneckerDeltas in following equation? k, p1, ...
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59 views

Understanding a “strange” output about a finite sum

Input: Sum[HarmonicNumber[k]/k^2, {k, 1, m}] That is $$\sum_{k = 1}^{m} \frac{H_k}{k^2}$$ Output I will attach a screenshot for I don't even know how to write ...
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1answer
41 views

Exponents manipulation

When I type(a^2)^s Mathematica does not give me $a^{2s}$ instead it gives ${(a^2)}^s$. Is there a way to make it print $a^{2s}$. It made some real difference where ...
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2answers
110 views

Implementing a formula from a paper

Is this:Table[Exp[-((1250^2) dism11[[n, m]])/Sum[dism11[[i, j]], {i, n, 1250}, {j, m, 1250}]], {n, 1, 1250}, {m,1, 1250}] a correct way to implement: I am kinda ...
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2answers
133 views

Exploring Matrix Powers with Wolfram (using Sum Notation)

I am trying to gain an intuition for what algebraically happens to a square matrix (say a $2$-dimensional square matrix) when it is successively multiplied by itself. I have used ...
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2answers
95 views

Does this sum converge, and why?

Mathematica says the following sum Sum[(mm Gamma[mm])/ Gamma[-(1/2) + mm] - (mm^(3/2) - (3 Sqrt[mm])/8 - (7 Sqrt[1/mm])/ 128), {mm, 1, \[Infinity]}] ...
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1answer
83 views

How can I calculate the Allan Variance of a list of Data?

I have a list with over 10.000 elements of data. Now I wanna calculate the Allan Variance of this Measurement. The Allan Variance is defined as following: $$\sigma_y^2(\tau)=\frac1{2\tau^2}\langle(x_{...
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52 views

Equations with Tensor product and Ket in Mathematica:

I tried to express this equation in Mathematica: I defined necessary things: ...
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84 views

Mathematica ruins domain after explicit summation?

I'm working with this function ...
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1answer
81 views

speed up symbolic summation

I have the following summation L=24; sind=Range[-Pi,Pi,2*Pi/L]; Sum[f, {x, sind}, {y, sind}, {x1, sind}, {y1, sind}, {x2, sind}, {y2, sind}] where ...
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1answer
34 views

Expand product of symbolic sums (with identically named indices)

I have an expression that is a product of two symbolic sums. Sum[a[k], {k, 1, n}]*Sum[b[k], {k, 1, n}] How can I expand this expression? I want to see something ...

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