Questions tagged [summation]
Questions using the Sum command, especially for series and other algebraic objects, and related functions such as SumConvergence
802
questions
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0answers
68 views
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}...
1
vote
0answers
37 views
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 ...
2
votes
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 $\sigma'_{-2k-1}(n) = \sum_{d|n, \text{d odd}} d^{-2k-1}$.
...
2
votes
1answer
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.
...
0
votes
1answer
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 ...
0
votes
1answer
51 views
Plot3d plots an empty graph [closed]
So I'm trying to graph a wave-type function using the following code:
...
3
votes
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:
...
1
vote
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
...
1
vote
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 ...
0
votes
1answer
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 ...
1
vote
3answers
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
$$
\sum_{m,n=1}^{\infty}\frac{1}{m^{4}+...
3
votes
0answers
96 views
Summation variables aren't recognised as dummy variables
I'm trying to write this expression
in Mathematica, and calculate the following quantity
However, when I tried the following
...
1
vote
0answers
43 views
Large and infinite sums evaluated numerically
I am interested to learn when and how Mathematica is able to evaluate large/infinite sums numerically in reasonable time. I have found that it can evaluate
$$
\sum_{l=1}^{\infty}e^{il/2}H_{0}^{(1)}(l)
...
0
votes
0answers
28 views
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.
...
0
votes
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 ...
0
votes
0answers
29 views
1
vote
1answer
35 views
ParallelSum issue inside package
I have the following very simple package with only one external function SumSeries[]:
...
1
vote
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 ...
0
votes
0answers
25 views
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
$$ I=\left(\int f(x)g(x) dx\right) * h $$
...
2
votes
3answers
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 ...
1
vote
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 ...
0
votes
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 ...
3
votes
2answers
105 views
1
vote
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
...
0
votes
1answer
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:
...
0
votes
1answer
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 $...
3
votes
0answers
51 views
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 ...
2
votes
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 ...
1
vote
0answers
27 views
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 ...
1
vote
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:
...
4
votes
2answers
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:
<...
1
vote
0answers
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= (...
0
votes
1answer
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).
0
votes
1answer
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, ...
0
votes
0answers
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 ...
1
vote
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?)
...
1
vote
1answer
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:
...
0
votes
0answers
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
...
0
votes
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 ...
2
votes
0answers
75 views
How to sum the KroneckerDelta[] in equation?
How to sum the KroneckerDeltas in following equation?
k, p1, ...
0
votes
1answer
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 ...
2
votes
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 ...
2
votes
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 ...
1
vote
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
...
3
votes
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]}]
...
2
votes
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_{...
0
votes
0answers
52 views
Equations with Tensor product and Ket in Mathematica:
I tried to express this equation in Mathematica:
I defined necessary things:
...
0
votes
2answers
84 views
0
votes
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 ...
0
votes
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 ...
